Understanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

%B Journal of the Mechanics and Physics of Solids %V 134 %P 103745 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022509619304065 %R https://doi.org/10.1016/j.jmps.2019.103745 %0 Journal Article %J Rendiconti del Circolo Matematico di Palermo Series 2 %D 2019 %T The Serre–Swan theorem for normed modules %A Danka Lučić %A Enrico Pasqualetto %B Rendiconti del Circolo Matematico di Palermo Series 2 %V 68 %P 385–404 %8 Aug %G eng %U https://doi.org/10.1007/s12215-018-0366-6 %R 10.1007/s12215-018-0366-6 %0 Conference Paper %B VIII International Conference on Computational Methods in Marine Engineering %D 2019 %T Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces %A Marco Tezzele %A Nicola Demo %A Gianluigi Rozza %XWe propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique. The ROM are based on a finite volume method (FV) to simulate the multi-phase incompressible flow around the deformed hulls. In previous works we studied the reduction of the parameter space in naval engineering through AS [38, 10] focusing on different parts of the hull. PODI and DMD have been employed for the study of fast and reliable shape optimization cycles on a bulbous bow in [9]. The novelty of this work is the simultaneous reduction of both the input parameter space and the output fields of interest. In particular AS will be trained computing the total drag resistance of a hull advancing in calm water and its gradients with respect to the input parameters. DMD will improve the performance of each simulation of the campaign using only few snapshots of the solution fields in order to predict the regime state of the system. Finally PODI will interpolate the coefficients of the POD decomposition of the output fields for a fast approximation of all the fields at new untried parameters given by the optimization algorithm. This will result in a non-intrusive data-driven numerical optimization pipeline completely independent with respect to the full order solver used and it can be easily incorporated into existing numerical pipelines, from the reference CAD to the optimal shape.

%B VIII International Conference on Computational Methods in Marine Engineering %G eng %0 Report %D 2019 %T The sharp quantitative isocapacitary inequality %A Guido De Philippis %A Michele Marini %A Ekaterina Mukoseeva %B arXiv preprint arXiv:1901.11309 %G eng %0 Report %D 2019 %T On the square distance function from a manifold with boundary %A Giovanni Bellettini %A Alaa Elshorbagy %XWe characterize arbitrary codimensional smooth manifolds $\mathcal{M}$ with boundary embedded in $\mathbb{R}^n$ using the square distance function and the signed distance function from $\mathcal{M}$ and from its boundary. The results are localized in an open set.

%G eng %U http://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf %0 Journal Article %J arXiv e-prints %D 2019 %T Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras %A Paolo Antonini %A Buss, Alcides %A Engel, Alexander %A Siebenand , Timo %K Mathematics - K-Theory and Homology %K Mathematics - Operator Algebras %XWe strengthen a result of Hanke–Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

%B arXiv e-prints %P arXiv:1905.07730 %8 May %G eng %0 Journal Article %J Rendiconti Lincei-Matematica e Applicazioni %D 2018 %T Second order differentiation formula on RCD(K, N) spaces %A Nicola Gigli %A Luca Tamanini %B Rendiconti Lincei-Matematica e Applicazioni %V 29 %P 377–386 %G eng %0 Report %D 2018 %T Second order differentiation formula on RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %G eng %0 Conference Paper %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %D 2018 %T Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition %A Nicola Demo %A Marco Tezzele %A Gianluca Gustin %A Gianpiero Lavini %A Gianluigi Rozza %X Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method. We use the free form deformation (FFD) for an automated perturbation of the shape, and the finite volume method to simulate the multiphase incompressible flow around the deformed hulls. Further computational reduction is done by the dynamic mode decomposition (DMD) technique: from few high dimensional snapshots, the system evolution is reconstructed and the final state of the simulation is faithfully approximated. Finally the global optimization algorithm iterates over the reduced space: the approximated drag and lift coefficients are projected to the hull surface, hence the resistance is evaluated for the new hulls until the convergence to the optimal shape is achieved. We will present the results obtained applying the described procedure to a typical Fincantieri cruise ship. %B Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research %I IOS Press %C Trieste, Italy %G eng %U http://ebooks.iospress.nl/publication/49229 %& 212 %R 10.3233/978-1-61499-870-9-212 %0 Journal Article %J Math. Mech. Solids %D 2018 %T Shape transitions in a soft incompressible sphere with residual stresses %A Davide Riccobelli %A Pasquale Ciarletta %B Math. Mech. Solids %I SAGE Publications Sage UK: London, England %V 23 %P 1507–1524 %G eng %0 Journal Article %J Journal of Nonlinear Mathematical Physics %D 2018 %T Singular Hartree equation in fractional perturbed Sobolev spaces %A Alessandro Michelangeli %A Alessandro Olgiati %A Raffaele Scandone %XWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

%B Journal of Nonlinear Mathematical Physics %I Taylor & Francis %V 25 %P 558-588 %G eng %U https://doi.org/10.1080/14029251.2018.1503423 %R 10.1080/14029251.2018.1503423 %0 Report %D 2018 %T On some rigorous aspects of fragmented condensation %A Daniele Dimonte %A Marco Falconi %A Alessandro Olgiati %G eng %U https://arxiv.org/abs/1809.03586 %0 Journal Article %J Journal of Mathematical Physics %D 2018 %T Spectral triples on the Jiang-Su algebra %A Jacopo Bassi %A Ludwik Dabrowski %B Journal of Mathematical Physics %V 59 %P 053507 %G eng %U https://doi.org/10.1063/1.5026311 %R 10.1063/1.5026311 %0 Report %D 2018 %T Stochastic homogenisation of free-discontinuity problems %A Filippo Cagnetti %A Gianni Dal Maso %A Lucia Scardia %A Caterina Ida Zeppieri %X In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas. %G en %U http://preprints.sissa.it/handle/1963/35309 %1 35617 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:16:27Z No. of bitstreams: 1 Cag-DM-Sca-Zep-Stochastic.pdf: 427225 bytes, checksum: 758a4e21e1c47b4a34c774f5d4bff8c2 (MD5) %0 Journal Article %J Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2018 %T Symplectic invariants for parabolic orbits and cusp singularities of integrable systems %A Alexey Bolsinov %A Lorenzo Guglielmi %A Elena Kudryavtseva %XWe discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

%B Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 376 %P 20170424 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0424 %R 10.1098/rsta.2017.0424 %0 Report %D 2017 %T Second order differentiation formula on compact RCD*(K,N) spaces %A Nicola Gigli %A Luca Tamanini %G eng %0 Report %D 2017 %T Self-Adjoint Extensions of Dirac Operator with Coulomb Potential %A Matteo Gallone %X In this note we give a concise review of the present state-of-art for the problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular scalar potential V(x) = Ø(x)I4. We try to follow the historical and conceptual path that leads to the present understanding of the problem and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35273 %1 35579 %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-02-17T06:59:43Z No. of bitstreams: 1 Gallone_preprint2017.pdf: 186169 bytes, checksum: aa5eaaac65f07802fc5a3842ace968b4 (MD5) %0 Report %D 2017 %T Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei %A Matteo Gallone %A Alessandro Michelangeli %X We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the KreĬn-Višik- Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neu- mann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the exten- sion, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension. %G en %U http://preprints.sissa.it/handle/1963/35287 %1 35592 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-06-05T06:42:39Z No. of bitstreams: 1 Coulomb_Gallone_Michelangeli_26_2017.pdf: 508858 bytes, checksum: 21c788d0de4fed88bee2e6fd5cd0849c (MD5) %0 Report %D 2017 %T Semistable Higgs Bundles on Calabi-Yau Manifolds %A Ugo Bruzzo %A Valeriano Lanza %A Alessio Lo Giudice %X We provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces. %G en %U http://preprints.sissa.it/handle/1963/35295 %1 35601 %2 Mathematics %4 1 %$ Submitted by mmarin@sissa.it (mmarin@sissa.it) on 2017-09-25T12:19:23Z No. of bitstreams: 1 SISSA_preprint_40-2017-MATE.pdf: 346868 bytes, checksum: 2ae5e19d45989bb2fa878236dd18d780 (MD5) %0 Journal Article %J Journal of Dynamical and Control Systems %D 2017 %T Small Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators %A Elisa Paoli %XWe compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

%B Journal of Dynamical and Control Systems %V 23 %P 111–143 %8 Jan %G eng %U https://doi.org/10.1007/s10883-016-9321-z %R 10.1007/s10883-016-9321-z %0 Journal Article %J J. Elast. %D 2017 %T Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth %A D. Ambrosi %A Pezzuto, S. %A Davide Riccobelli %A Stylianopoulos, T. %A Pasquale Ciarletta %B J. Elast. %I Springer Netherlands %V 129 %P 107–124 %G eng %0 Book Section %B Numerical Mathematics and Advanced Applications - ENUMATH 2017 %D 2017 %T A Spectral Element Reduced Basis Method in Parametric CFD %A Martin W. Hess %A Gianluigi Rozza %XWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

%B Numerical Mathematics and Advanced Applications - ENUMATH 2017 %I Springer %V 126 %G eng %& A Spectral Element Reduced Basis Method in Parametric CFD %0 Conference Paper %B Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, in press %D 2017 %T A Spectral Element Reduced Basis Method in Parametric CFD %A Martin W. Hess %A Gianluigi Rozza %B Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, in press %G eng %0 Journal Article %D 2017 %T Spectral Properties of the 2+1 Fermionic Trimer with Contact Interactions %A Simon Becker %A Alessandro Michelangeli %A Andrea Ottolini %X We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise and prove the finiteness of the discrete spectrum, qualify the angular symmetry of the eigenfunctions, and prove the monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence of bound states in a physically relevant regime of masses. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35303 %1 35609 %2 Mathematics %4 1 %$ Submitted by mmarin@sissa.it (mmarin@sissa.it) on 2018-01-04T08:57:37Z No. of bitstreams: 1 SISSA_preprint_61-2017-MATE.pdf: 465833 bytes, checksum: bc2bbd7578ccfcd69ca2a33a2fc3adb0 (MD5) %0 Journal Article %J Meccanica %D 2017 %T Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler %A Paolo Gidoni %A Antonio DeSimone %XWe formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

%B Meccanica %V 52 %P 587–601 %8 Feb %G eng %U https://doi.org/10.1007/s11012-016-0408-0 %R 10.1007/s11012-016-0408-0 %0 Journal Article %J Inventiones Mathematicae %D 2017 %T Symplectic geometry of the moduli space of projective structures in homological coordinates %A Marco Bertola %A Dmitry Korotkin %A Chaya Norton %B Inventiones Mathematicae %P 1–56 %8 06 %G eng %U https://arxiv.org/abs/1506.07918 %0 Report %D 2016 %T Second-order structured deformations %A Ana Cristina Barroso %A Jose Matias %A Marco Morandotti %A David R. Owen %I SISSA %G en %1 35497 %2 Mathematics %4 1 %$ Submitted by Lucio Lubiana (lubiana@sissa.it) on 2016-07-08T11:42:55Z No. of bitstreams: 1 Morandott-2oStD.pdf: 385787 bytes, checksum: 31ae44cb708c09f82aba2f6ea5e73248 (MD5) %0 Conference Paper %B The 26th International Ocean and Polar Engineering Conference %D 2016 %T Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %A Massimiliano Berti %B The 26th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %V 3 %P 511–518 %G eng %0 Journal Article %J Int. Math. Res. Not. %D 2016 %T Simple Lie Algebras and Topological ODEs %A Marco Bertola %A Boris Dubrovin %A Di Yang %B Int. Math. Res. Not. %V 2016 %G eng %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2016 %T On Sobolev instability of the interior problem of tomography %A Marco Bertola %A Alexander Katsevich %A Alexander Tovbis %B Journal of Mathematical Analysis and Applications %G eng %0 Thesis %D 2016 %T Some results on quasistatic evolution problems for unidirectional processes %A Vito Crismale %I SISSA %G en %1 35522 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by vcrisma@sissa.it (vcrisma@sissa.it) on 2016-09-18T20:26:55Z No. of bitstreams: 1 TesiPHD.pdf: 1721272 bytes, checksum: 95ef69bafc860616d3cdb08901da7ffb (MD5) %0 Thesis %D 2016 %T Some results on the mathematical analysis of crack problems with forces applied on the fracture lips %A Stefano Almi %K Fracture mechanics %X This thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u. %I SISSA %G en %1 35503 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2016-08-09T10:34:01Z No. of bitstreams: 1 Almi-PhDThesis.pdf: 2060635 bytes, checksum: 5fab9efd5312430a0c9e57282df75694 (MD5) %0 Journal Article %J Communications in Partial Differential Equations %D 2016 %T Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds %A Ugo Boscain %A Dario Prandi %A M. Seri %XWe study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

%B Communications in Partial Differential Equations %I Taylor & Francis %V 41 %P 32-50 %G eng %U https://doi.org/10.1080/03605302.2015.1095766 %R 10.1080/03605302.2015.1095766 %0 Report %D 2016 %T On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension %A Stefano Bianchini %A Elio Marconi %XWe prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

%I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35209 %1 35508 %2 Mathematics %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-09-06T09:18:03Z No. of bitstreams: 1 1608.02811v1.pdf: 591028 bytes, checksum: 069b218b01f350df6db7904e245ef701 (MD5) %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index %A Benvenuti, Sergio %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %XWe explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

%B Journal of High Energy Physics %V 2016 %P 53 %8 Sep %G eng %U https://doi.org/10.1007/JHEP09(2016)053 %R 10.1007/JHEP09(2016)053 %0 Journal Article %J Annali della Scuola Normale Superiore di Pisa. Classe di scienze %D 2016 %T Symmetry properties of some solutions to some semilinear elliptic equations %A Farina, Alberto %A Andrea Malchiodi %A Matteo Rizzi %B Annali della Scuola Normale Superiore di Pisa. Classe di scienze %I Classe di Scienze %V 16 %P 1209–1234 %G eng %0 Report %D 2015 %T Schödinger operators on half-line with shrinking potentials at the origin %A Gianfausto Dell'Antonio %A Alessandro Michelangeli %X We discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34439 %1 34566 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-02-09T07:28:40Z No. of bitstreams: 1 SISSA_preprint_06-2015-MATE.pdf: 177243 bytes, checksum: 383296953d36b4cec0cb4cfb55e95d7f (MD5) %0 Report %D 2015 %T Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity %A Lucia Tealdi %A Giovanni Bellettini %A Maurizio Paolini %XWe address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34483 %1 34670 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-08-07T16:06:48Z No. of bitstreams: 1 bellettini_paolini_tealdi_semicartesian.pdf: 623410 bytes, checksum: 871f66c4686a39ad7d1bc996f0e2b0aa (MD5) %0 Thesis %D 2015 %T Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings. %A Gabriele Mancini %K Moser-Trudinger %X We investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems. %I SISSA %G en %1 34738 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-09-22T12:27:17Z No. of bitstreams: 1 tesi4.pdf: 1376221 bytes, checksum: cfc85996d91a3384e94546a64bf8c479 (MD5) %0 Report %D 2015 %T Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results %A Gabriele Mancini %XWe prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34489 %1 34672 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-11T09:06:30Z No. of bitstreams: 1 art4.pdf: 352978 bytes, checksum: 4e081003a6b037544c46954c3d44b826 (MD5) %0 Thesis %D 2015 %T Some results on anisotropic mean curvature and other phase-transition problems %A Stefano Amato %K Anisotropic mean curvature %X The present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions. %I SISSA %G en %1 34733 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Stefano Amato (samato@sissa.it) on 2015-09-21T12:36:18Z No. of bitstreams: 1 tesi.pdf: 1566254 bytes, checksum: be7cf105a787693fd374acc1afe44fc3 (MD5) %0 Report %D 2015 %T Stability of closed gaps for the alternating Kronig-Penney Hamiltonian %A Alessandro Michelangeli %A Domenico Monaco %X We consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34460 %1 34629 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-04-01T14:57:03Z No. of bitstreams: 1 SISSA_preprint_16-2015-MATE.pdf: 349807 bytes, checksum: f5e6dacd85fb41c96420795cc37cc12c (MD5) %0 Report %D 2015 %T Stability of the (2+2)-fermionic system with zero-range interaction %A Alessandro Michelangeli %A Paul Pfeiffer %X We introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the the celebrated (and ubiquitous, in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Visik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system. %G en %U http://urania.sissa.it/xmlui/handle/1963/34474 %1 34649 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Alessandro Michelangeli (alemiche@sissa.it) on 2015-06-24T10:47:38Z No. of bitstreams: 1 sissa-preprint-29-2015-mate.pdf: 827153 bytes, checksum: e5268c2d26f348929a3c532f9ffd3097 (MD5) %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2015 %T Stable regular critical points of the Mumford-Shah functional are local minimizers %A Marco Bonacini %A Massimiliano Morini %K Mumford-Shah functional %XIn this paper it is shown that any regular critical point of the Mumford–Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$

-topology. A global minimality result in small tubular neighborhoods of the discontinuity set is also established.

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 471 %P 20150054 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 %R 10.1098/rspa.2015.0054 %0 Journal Article %D 2015 %T Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations %A Francesco Ballarin %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %X In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. %I Wiley %G en %U http://urania.sissa.it/xmlui/handle/1963/34701 %1 34915 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-10-22T11:39:58Z No. of bitstreams: 1 IJNME_2014.pdf: 6761966 bytes, checksum: ad65f2c4d2dbd30a4a1590ff42ee49a0 (MD5) %R 10.1002/nme.4772 %0 Journal Article %J Acta Applicandae Mathematicae, vol. 137, Issue 1, 2015, pages: 185-203 %D 2015 %T Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry %A Domenico Monaco %A Gianluca Panati %XWe describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, called the Bloch bundle. The rôle of additional Z_2-symmetries, as time-reversal and space-reflection symmetry, is discussed, showing how time-reversal symmetry implies the triviality of the Bloch bundle, both in the bosonic and in the fermionic case. Moreover, the same Z_2-symmetry allows to define a finer notion of isomorphism and, consequently, to define new topological invariants, which agree with the indices introduced by Fu, Kane and Mele in the context of topological insulators.

%B Acta Applicandae Mathematicae, vol. 137, Issue 1, 2015, pages: 185-203 %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34468 %1 34642 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Domenico Monaco (dmonaco@sissa.it) on 2015-05-15T10:12:11Z No. of bitstreams: 1 CalaGonone.pdf: 500680 bytes, checksum: 00aa2839c4d737f45da3d828e5cc0a53 (MD5) %R 10.1007/s10440-014-9995-8 %0 Journal Article %D 2014 %T SBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations %A Stefano Bianchini %X We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34691 %1 34904 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T08:51:26Z No. of bitstreams: 1 proceeding.DFDE11.pdf: 401448 bytes, checksum: 0002408d841699f963dfb817ed96e577 (MD5) %R 10.1007/s10958-014-2022-9 %0 Journal Article %D 2014 %T Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K Gamma-convergence, Cahn-Hilliard functional, phase transitions %X The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values. %I SISSA %G en %U http://hdl.handle.net/1963/7390 %1 7439 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-06-19T16:24:43Z No. of bitstreams: 1 DM-Fon-Leo-14-sissa.pdf: 409621 bytes, checksum: 40ba0baf0686b18dcd89582772f376b5 (MD5) %0 Journal Article %D 2014 %T Semiclassical limit of focusing NLS for a family of square barrier initial data %A Robert Jenkins %A Kenneth McLaughlin %X The small dispersion limit of the focusing nonlinear Schrödinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data,the family of square barriers,ψ 0(x) = qχ[-L,L] for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O(1) maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data. %I Wiley Periodicals %G en %U http://urania.sissa.it/xmlui/handle/1963/35066 %1 35301 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-30T14:57:14Z No. of bitstreams: 1 preprint2014.pdf: 5320973 bytes, checksum: 457b6c96cf2335a7c55084d85eed3dbc (MD5) %R 10.1002/cpa.21494 %0 Journal Article %D 2014 %T Shape control of active surfaces inspired by the movement of euglenids %A Marino Arroyo %A Antonio DeSimone %X We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35118 %1 35375 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-03T09:19:38Z (GMT) No. of bitstreams: 0 %R 10.1016/j.jmps.2013.09.017 %0 Journal Article %D 2014 %T Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows %A Francesco Ballarin %A Andrea Manzoni %A Gianluigi Rozza %A Sandro Salsa %X Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34698 %1 34914 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T11:24:27Z (GMT) No. of bitstreams: 0 %R 10.1007/s10915-013-9807-8 %0 Journal Article %J Comm. Pure Appl. Math. %D 2014 %T Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach %A Marco Bertola %A Alexander Katsevich %A Alexander Tovbis %B Comm. Pure Appl. Math. %G eng %0 Journal Article %D 2014 %T Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34546 %1 34771 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-09-28T10:16:32Z No. of bitstreams: 1 art2014.pdf: 600092 bytes, checksum: 8a020f470fff4ce83b5d820436def73f (MD5) %R 10.1007/JHEP07(2014)141 %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2014 %T Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms %A Sara Daneri %A Aldo Pratelli %XWe show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the W1,p norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

%B Annales de l'Institut Henri Poincare (C) Non Linear Analysis %V 31 %P 567 - 589 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144913000711 %R https://doi.org/10.1016/j.anihpc.2013.04.007 %0 Report %D 2014 %T Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics %A Giuliano Lazzaroni %A Riccarda Rossi %A Marita Thomas %A Rodica Toader %X This note deals with the analysis of a model for partial damage, where the rateindependent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1] with the methods from Lazzaroni/Rossi/Thomas/Toader [2] and extend the analysis to the setting of inhomogeneous time-dependent Dirichlet data. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7463 %1 7566 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-10-23T09:01:52Z No. of bitstreams: 1 MURPHYS_LRTT14_SISSA-preprint(1).pdf: 246259 bytes, checksum: a67369f4eab98d39fb2165d882d97592 (MD5) %0 Journal Article %D 2014 %T Some remarks on the seismic behaviour of embedded cantilevered retaining walls %A Riccardo Conti %A F. Burali D'Arezzo %A Giulia M.B. Viggiani %X This paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls. %I Thomas Telford %G en %U http://urania.sissa.it/xmlui/handle/1963/35073 %1 35308 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-30T17:34:56Z No. of bitstreams: 1 art2014.pdf: 1304935 bytes, checksum: 2618504941effc8eed6dddb1077d8916 (MD5) %R 10.1680/geot.13.P.031 %0 Journal Article %D 2014 %T Spontaneous division and motility in active nematic droplets %A Luca Giomi %A Antonio DeSimone %X We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number. %I American Physical Society %G en %U http://urania.sissa.it/xmlui/handle/1963/34902 %1 35107 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-03T14:40:44Z No. of bitstreams: 1 preprint2014.pdf: 4005398 bytes, checksum: eebaadedd03c1077a9cb2a209b5abdcc (MD5) %R 10.1103/PhysRevLett.112.147802 %0 Journal Article %J Advances in Calculus of Variations %D 2014 %T Stability of equilibrium configurations for elastic films in two and three dimensions %A Marco Bonacini %K Epitaxially strained elastic films %XWe establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

%B Advances in Calculus of Variations %I SISSA %V 8 %P 117-153 %8 01/2014 %G en %U https://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml %N 2 %1 6997 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Marco Bonacini (mbonacin@sissa.it) on 2013-08-07T11:12:48Z No. of bitstreams: 1 films.pdf: 595689 bytes, checksum: 009553ee1f902e6e6984675ad0cf70b6 (MD5) %& 117 %R https://doi.org/10.1515/acv-2013-0018 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering %D 2014 %T Stabilized reduced basis method for parametrized advection-diffusion PDEs %A Pacciarini, P. %A Gianluigi Rozza %XIn this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

%B Computer Methods in Applied Mechanics and Engineering %V 274 %P 1–18 %G eng %R 10.1016/j.cma.2014.02.005 %0 Conference Paper %B 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 %D 2014 %T Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts %A Pacciarini, P. %A Gianluigi Rozza %XAdvection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

%B 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 %P 5614–5624 %G eng %U https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf %0 Report %D 2014 %T Steady nearly incompressible vector elds in 2D: chain rule and renormalization %A Stefano Bianchini %A N.A. Gusev %I SISSA %G en %1 7464 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-08-13T07:08:46Z No. of bitstreams: 1 main_stefano(1).pdf: 631783 bytes, checksum: 3ac150a4fb3cb33ebaf5273751dfdf27 (MD5) %0 Journal Article %D 2014 %T The stringy instanton partition function %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit C^2/Z_2 the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants of P^1 x C^2. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34589 %1 34796 %2 Physics %4 2 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-09-28T14:48:41Z No. of bitstreams: 1 art2014.pdf: 719350 bytes, checksum: 2c296ad8eb7995f07c16f6d4e36c6813 (MD5) %R 10.1007/JHEP01(2014)038 %0 Report %D 2014 %T Structure of classical (finite and affine) W-algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X First, we derive an explicit formula for the Poisson bracket of the classical finite W-algebra W^{fin}(g,f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f. On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W-algebra W(g,f). As an immediate consequence, we obtain a Poisson algebra isomorphism between W^{fin}(g,f) and the Zhu algebra of W(g,f). We also study the generalized Miura map for classical W-algebras. %I SISSA %G en %U http://hdl.handle.net/1963/7314 %1 7359 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2014-04-04T09:52:02Z No. of bitstreams: 1 1404.0715v1.pdf: 386481 bytes, checksum: bafb532b11dfa1100008853a1f4cd543 (MD5) %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2014 %T Structure of entropy solutions to general scalar conservation laws in one space dimension %A Stefano Bianchini %A Lei Yu %B Journal of Mathematical Analysis and Applications %I SISSA %V 428 %P 356-386 %8 08/2015 %G en %U https://www.sciencedirect.com/science/article/pii/S0022247X15002218 %N 1 %1 7305 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-10T11:39:18Z No. of bitstreams: 1 Global structure of entropy solutions to scalar conservation laws.ref.pdf: 464993 bytes, checksum: 9b83b6f3f845eda8eb202f0748617756 (MD5) %& 356 %R https://doi.org/10.1016/j.jmaa.2015.03.006 %0 Journal Article %D 2014 %T Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch %A Alessandro Lucantonio %A Paola Nardinocchi %A Howard A. Stone %X It has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch. %I American Institute of Physics %G en %U http://urania.sissa.it/xmlui/handle/1963/35113 %1 35370 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:28:53Z No. of bitstreams: 1 art2014.pdf: 777840 bytes, checksum: 2362b6250fd872264208d0d3b846a551 (MD5) %R 10.1063/1.4866576 %0 Journal Article %D 2014 %T Swelling-induced and controlled curving in layered gel beams %A Alessandro Lucantonio %A Paola Nardinocchi %A Matteo Pezzulla %X We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method. %I Royal Society of London %G en %U http://urania.sissa.it/xmlui/handle/1963/34987 %1 35229 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2015-11-12T09:25:24Z (GMT) No. of bitstreams: 0 %R 10.1098/rspa.2014.0467 %0 Journal Article %D 2013 %T Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces %A Ugo Boscain %A Dario Prandi %G eng %R 10.1016/j.jde.2015.10.011 %0 Thesis %D 2013 %T Semistability and Decorated Bundles %A Andrea Pustetto %K Decorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf %X This thesis is devoted to the study of semistability condition of type t=(a,b,c,N) decorated bundles and sheaves in order to better understand and simplify it. We approach the problem in two different ways: on one side we “enclose” the above semistability condition between a stronger semistability condition (\epsilon-semistability) and a weaker one (k-semistability), on the other side we try, and succeed for the case of a = 2, to bound the length of weighted filtrations on which one checks the semistability condition. %I SISSA %G en %U http://hdl.handle.net/1963/7130 %1 7132 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrea Pustetto (apustett@sissa.it) on 2013-09-25T09:47:01Z No. of bitstreams: 1 Semistability and Decorated Bundles.pdf: 829003 bytes, checksum: 22aa7f058a1945c70a0e0d29b46829e3 (MD5) %0 Journal Article %D 2013 %T Softly Constrained Films %A Luca Giomi %X The shape of materials is often subject to a number of geometric constraints\r\nthat limit the size of the system or fix the structure of its boundary. In soft\r\nand biological materials, however, these constraints are not always hard, but\r\nare due to other physical mechanisms that affect the overall force balance. A\r\ncapillary film spanning a flexible piece of wire or a cell anchored to a\r\ncompliant substrate by mean of adhesive contacts are examples of these softly\r\nconstrained systems in the macroscopic and microscopic world. In this article I\r\nreview some of the important mathematical and physical developments that\r\ncontributed to our understanding of shape formation in softly constrained films\r\nand their recent application to the mechanics of adherent cells. %I SISSA %G en %U http://hdl.handle.net/1963/6563 %1 6518 %2 Mathematics %4 2 %# FIS/02 FISICA TEORICA, MODELLI E METODI MATEMATICI %$ Submitted by Luca Giomi (lgiomi@sissa.it) on 2013-04-04T08:04:08Z\nNo. of bitstreams: 1\n1304.1077v1.pdf: 4248769 bytes, checksum: c955d3de3233f3619d546d93dab34c63 (MD5) %0 Thesis %D 2013 %T Some models of crack growth in brittle materials %A Simone Racca %K Quasi-static crack evolution %I SISSA %G en %1 7205 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Simone Racca (sracca@sissa.it) on 2013-10-23T13:11:13Z No. of bitstreams: 1 Racca_PhDThesis.pdf: 1710871 bytes, checksum: ea174e98f8849253e71cdefa52c6c8b8 (MD5) %] Introduction Chapter 1. Preliminaries Chapter 2. A viscosity-driven crack evolution Chapter 3.A variational model for the quasi-static growth of fractional dimensional brittle fractures Chapter 4. A model for crack growth with branching and kinking Bibliography %0 Journal Article %D 2013 %T Some open problems %A Andrei A. Agrachev %K Geometry %X We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry. %I SISSA %G en %U http://hdl.handle.net/1963/7070 %1 7064 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-09-16T09:39:55Z No. of bitstreams: 1 1304.2590v2.pdf: 169033 bytes, checksum: 43fab332ae3bb82c336a19ab7013c373 (MD5) %0 Journal Article %J Discrete Contin. Dyn. Syst. Ser. S %D 2013 %T Some remarks on the viscous approximation of crack growth %A Giuliano Lazzaroni %A Rodica Toader %K Variational models %XWe describe an existence result for quasistatic evolutions of cracks in antiplane elasticity obtained in [16] by a vanishing viscosity approach, with free (but regular enough) crack path. We underline in particular the motivations for the choice of the class of admissible cracks and of the dissipation potential. Moreover, we extend the result to a model with applied forces depending on time.

%B Discrete Contin. Dyn. Syst. Ser. S %I SISSA %V 6 %G en %U http://hdl.handle.net/1963/4206 %1 3945 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-23T10:54:36Z No. of bitstreams: 1 Lazzaroni_Toader_24_M.pdf: 225564 bytes, checksum: 4c5000d79e83902639a8efb34ba9c0c8 (MD5) %& 131-146 %0 Thesis %D 2013 %T Some topics on Higgs bundles over projective varieties and their moduli spaces %A Alessio Lo Giudice %K Algebraic Geometry, Moduli spaces, Vector bundles %X In this thesis we study vector bundles on projective varieties and their moduli spaces. In Chapters 2, 3 and 4 we recall some basic notions as Higgs bundles, decorated bundles and generalized parabolic sheaves and introduce the problem we want to study. In chapter 5, we study Higgs bundles on nodal curves. After moving the problem on the normalization of the curve, starting from a Higgs bundle we obtain a generalized parabolic Higgs bundle. Using decorated bundles we are able to construct a projective moduli space which parametrizes equivalence classes of Higgs bundles on a nodal curve X. This chapter is an extract of a joint work with Andrea Pustetto Later on Chapter 6 is devoted to the study of holomorphic pairs (or twisted Higgs bundles) on elliptic curve. Holomorphic pairs were introduced by Nitsure and they are a natural generalization of the concept of Higgs bundles. In this Chapter we extend a result of E. Franco, O. Garc\'ia-Prada And P.E. Newstead valid for Higgs bundles to holomorphic pairs. Finally the last Chapter describes a joint work with Professor Ugo Bruzzo. We study Higgs bundles over varieties with nef tangent bundle. In particular generalizing a result of Nitsure we prove that if a Higgs bundle $(E,\phi)$ over the variety X with nef tangent remains semisatble when pulled-back to any smooth curve then it discrimiant vanishes. %I SISSA %G en %1 7134 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Alessio Lo Giudice (logiudic@sissa.it) on 2013-09-25T11:22:08Z No. of bitstreams: 1 Some topics on Higgs bundles over projective varieties and their moduli spaces .pdf: 666905 bytes, checksum: 58cf6bb5b212512b46c870b0d955a865 (MD5) %0 Journal Article %J J. Stat. Phys. %D 2013 %T Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes %A Marco Bertola %A Buckingham, R. %A Lee, S. Y. %A Pierce, V. %B J. Stat. Phys. %V 153 %P 654–697 %G eng %U http://dx.doi.org/10.1007/s10955-013-0845-2 %R 10.1007/s10955-013-0845-2 %0 Report %D 2013 %T The splitting theorem in non-smooth context %A Nicola Gigli %X We prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N −1)$ space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence. %G en %U http://preprints.sissa.it/handle/1963/35306 %1 35613 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-02-23T12:45:43Z No. of bitstreams: 1 Splittingmms-submitted.pdf: 826242 bytes, checksum: 0395e29f7f4d768880e012ef1a77073a (MD5) %0 Journal Article %J IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %D 2013 %T Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control %A Claudio Altafini %A Francesco Ticozzi %A K. Nishio %X In this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control %B IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %G en %U http://hdl.handle.net/1963/6503 %1 6448 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:06:12Z (GMT) No. of bitstreams: 0 %R 10.1109/TAC.2012.2206713 %0 Journal Article %J Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %D 2013 %T A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K Unsteady ship-wave interaction %XWe present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

%B Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %I SISSA %G en %U http://hdl.handle.net/1963/5669 %1 5457 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-03-16T11:19:51Z\\nNo. of bitstreams: 1\\nMolaHeltaiDeSimone-2012-aa.pdf: 1981527 bytes, checksum: 8a82da009242da0cf884e2c7f04009a6 (MD5) %0 Journal Article %J Applicable Analysis %D 2013 %T Stable determination of a body immersed in a fluid: the nonlinear stationary case %A Andrea Ballerini %XWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier–Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log–log type.

%B Applicable Analysis %I Taylor & Francis %V 92 %P 460-481 %G eng %U https://doi.org/10.1080/00036811.2011.628173 %R 10.1080/00036811.2011.628173 %0 Journal Article %J SIAM Journal on Numerical Analysis %D 2013 %T Stochastic optimal robin boundary control problems of advection-dominated elliptic equations %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %X In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided. %B SIAM Journal on Numerical Analysis %V 51 %P 2700–2722 %G eng %R 10.1137/120884158 %0 Journal Article %J J. Math. Phys. %D 2013 %T Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Math. Phys. %V 54 %P 043517, 25 %G eng %0 Thesis %D 2013 %T The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension %A Lei Yu %X This thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws. %I SISSA %G en %1 7210 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lei Yu (yulei@sissa.it) on 2013-10-23T15:42:25Z No. of bitstreams: 1 Thesis_main.pdf: 960810 bytes, checksum: d3e2f04a4bb7cc2c30ba82507d536edc (MD5) %] Contents 0.1 HyperbolicConservationLaws. .......................... 1 0.2 SBV and SBV-like regularity ........................... 3 0.3 Global structure of BV solutions ......................... 6 0.4 Main notations ................................... 9 1 Preliminary results 11 1.1 BV and SBV functions............................... 11 1.2 Coarea formula for BV function.......................... 15 1.3 The singular conservation law........................... 16 1.3.1 The Riemann problem........................... 17 1.3.2 Front tracking algorithm.......................... 18 1.3.3 Uniform boundedness estimates on the speed of wave fronts . . . . . . 19 1.4 The Cauchy problem for systems ......................... 21 1.4.1 Solution of Riemann problem....................... 22 1.4.2 Construction of solution by wave-front tracking approximation . . . . 26 2 SBV-like regularity for strictly hyperbolic systems of conservation laws 33 2.1 Overview of the chapter .............................. 33 2.2 The scalar case ................................... 34 2.3 Notations and settings for general systems.................... 37 2.3.1 Preliminary notation............................ 37 2.3.2 Construction of solutions to the Riemann problem . . . . . . . . . . . 38 2.3.3 Cantor part of the derivative of characteristic for i-th waves . . . . . 39 2.4 Main SBV regularity argument .......................... 40 2.5 Review of wave-front tracking approximation for general system . . . . . . . . 41 2.5.1 Description of the wave-front tracking approximation . . . . . . . . . . 42 2.5.2 Jump part of i-th waves.......................... 43 2.6 Proof of Theorem2.4.1............................... 46 2.6.1 Decay estimate for positive waves..................... 46 2.6.2 Decay estimate for negative waves .................... 47 2.7 SBV regularity for the i-th component of the i-th eigenvalue . . . . . . . . . 54 i CONTENTS 3 Global structure of admissible BV solutions to the piecewise genuinely nonlinear system 57 3.1 Description of wave-front tracking approximation . . . . . . . . . . . . . . . . 62 3.2 Construction of subdiscontinuity curves ..................... 63 3.3 Proof of the main theorems ............................ 67 3.4 A counterexample on general strict hyperbolic systems . . . . . . . . . . . . . 71 4 Global structure of entropy solutions to general scalar conservation law 75 4.1 Overview ...................................... 75 4.2 Estimates on the level sets of the front tracking approximations . . . . . . . . 76 4.2.1 Bounds on the initial points of the boundary curves of level sets . . . 77 4.2.2 Bound estimates on the derivative of the boundary curves of level sets 77 4.3 Level sets in the exact solutions.......................... 78 4.4 Lagrangian representative for the entropy solution . . . . . . . . . . . . . . . 84 4.5 Pointwise structure................................. 88 %0 Journal Article %J Discrete & Continuous Dynamical Systems - A %D 2013 %T Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions %A Alberto Boscaggin %A Fabio Zanolin %K lower and upper solutions %K parameter dependent equations %K Periodic solutions %K Poincaré-Birkhoff twist theorem %K subharmonic solutions %XWe study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.

%B Discrete & Continuous Dynamical Systems - A %V 33 %P 89 %G eng %U http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f %R 10.3934/dcds.2013.33.89 %0 Report %D 2013 %T On Sudakov's type decomposition of transference plans with norm costs %A Stefano Bianchini %A Sara Daneri %I SISSA %G en %U http://hdl.handle.net/1963/7206 %1 7234 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-11-08T11:08:16Z No. of bitstreams: 1 Sudakov_160813 (1).pdf: 1030337 bytes, checksum: 121734a60b7c507acb1e0ca656676a37 (MD5) %0 Report %D 2013 %T Symplectic instanton bundles on P3 and 't Hooft instantons %A Ugo Bruzzo %A Dimitri Markushevich %A Alexander Tikhomirov %X We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of 't Hooft instantons. %I arXiv:1312.5554 [math.AG] %G en %U http://urania.sissa.it/xmlui/handle/1963/34486 %1 34675 %2 Mathematics %4 1 %# MAT/03 %$ Submitted by Ugo Bruzzo (bruzzo@sissa.it) on 2015-08-07T20:57:05Z No. of bitstreams: 1 Symplectic_instantons_II-rev-dec2014.pdf: 340035 bytes, checksum: 8d0a2dfeea126810645c06e8b6352903 (MD5) %0 Journal Article %J Communications in Mathematical Physics 313 (2012) 1-33 %D 2012 %T SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension %A Stefano Bianchini %A Laura Caravenna %B Communications in Mathematical Physics 313 (2012) 1-33 %I Springer %G en_US %U http://hdl.handle.net/1963/4091 %1 313 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-19T09:31:49Z\\r\\nNo. of bitstreams: 1\\r\\nBianchini_Caravenna_71M_2010.pdf: 591519 bytes, checksum: 388c1d8be60af95097574c718b4708b2 (MD5) %R 10.1007/s00220-012-1480-5 %0 Journal Article %J Siam Journal on Mathematical Analysis %D 2012 %T SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x) %A Stefano Bianchini %A Daniela Tonon %B Siam Journal on Mathematical Analysis %I SISSA %V 44 %P 2179-2203 %G en %U http://hdl.handle.net/20.500.11767/14066 %N 3 %1 3890 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-20T13:28:47Z\r\nNo. of bitstreams: 1\r\nBianchini_Tonon_13M.pdf: 249849 bytes, checksum: 461aecb2ce41d2bff011ba0062ed1cfb (MD5) %R 10.1137/110827272 %0 Journal Article %J Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388 %D 2012 %T SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension %A Stefano Bianchini %K Hyperbolic systems %X The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity %B Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388 %I Elsevier %G en %U http://hdl.handle.net/1963/6535 %1 6510 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-03-21T08:22:40Z\nNo. of bitstreams: 0 %R 10.1016/S0252-9602(12)60024-1 %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste %D 2012 %T SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension %A Stefano Bianchini %A Lei Yu %B Rend. Istit. Mat. Univ. Trieste %V 44 %P 439–472 %G eng %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2012 %T SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian %A Stefano Bianchini %A Daniela Tonon %B Journal of Mathematical Analysis and Applications %I SISSA %V 391 %P 190-208 %G en %U http://hdl.handle.net/20.500.11767/13909 %N 1 %1 4352 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-07T11:24:37Z\\r\\nNo. of bitstreams: 1\\r\\n45M_Tonon_Bianchini.pdf: 179519 bytes, checksum: c157fc19ae52c2fb8bcd2ca28815d26e (MD5) %R 10.1016/j.jmaa.2012.02.017 %0 Journal Article %J Discrete & Continuous Dynamical Systems - A %D 2012 %T Second order approximations of quasistatic evolution problems in finite dimension %A Virginia Agostiniani %K discrete approximations %K perturbation methods %K saddle-node bifurcation %K Singular perturbations %K vanishing viscosity %XIn this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

%B Discrete & Continuous Dynamical Systems - A %V 32 %P 1125 %G eng %U http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8 %R 10.3934/dcds.2012.32.1125 %0 Journal Article %J Journal of Biological Dynamics %D 2012 %T Self-propelled micro-swimmers in a Brinkman fluid %A Marco Morandotti %XWe prove an existence, uniqueness, and regularity result for the motion of a self-propelled micro-swimmer in a particulate viscous medium, modelled as a Brinkman fluid. A suitable functional setting is introduced to solve the Brinkman system for the velocity field and the pressure of the fluid by variational techniques. The equations of motion are written by imposing a self-propulsion constraint, thus allowing the viscous forces and torques to be the only ones acting on the swimmer. From an infinite-dimensional control on the shape of the swimmer, a system of six ordinary differential equations for the spatial position and the orientation of the swimmer is obtained. This is dealt with standard techniques for ordinary differential equations, once the coefficients are proved to be measurable and bounded. The main result turns out to extend an analogous result previously obtained for the Stokes system.

%B Journal of Biological Dynamics %I Taylor & Francis %V 6 %P 88-103 %G eng %U https://doi.org/10.1080/17513758.2011.611260 %R 10.1080/17513758.2011.611260 %0 Journal Article %J International Journal Numerical Methods Biomedical Engineering %D 2012 %T Simulation-based uncertainty quantification of human arterial network hemodynamics %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %K uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction %X This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time. %B International Journal Numerical Methods Biomedical Engineering %I Wiley %G en %1 6467 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-03-07T12:33:02Z\nNo. of bitstreams: 1\nreport.pdf: 1605405 bytes, checksum: bb12cf074ce32a80567a0cde0c0861db (MD5) %0 Journal Article %J Nonlinearity %D 2012 %T Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential %A Massimiliano Berti %A Philippe Bolle %X We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d ≥ 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11]. © 2012 IOP Publishing Ltd. %B Nonlinearity %V 25 %P 2579-2613 %G eng %R 10.1088/0951-7715/25/9/2579 %0 Journal Article %J Int Math Res Notices (2012) 2012 (6): 1352-1413 %D 2012 %T Solving the Sixth Painlevé Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae %A Davide Guzzetti %X The critical behavior of a three real parameter class of solutions of the\\r\\nsixth Painlev\\\\\\\'e equation is computed, and parametrized in terms of monodromy\\r\\ndata of the associated $2\\\\times 2$ matrix linear Fuchsian system of ODE. The\\r\\nclass may contain solutions with poles accumulating at the critical point. The\\r\\nstudy of this class closes a gap in the description of the transcendents in one\\r\\nto one correspondence with the monodromy data. These transcendents are reviewed in the paper. Some formulas that relate the monodromy data to the critical behaviors of the four real (two complex) parameter class of solutions are\\r\\nmissing in the literature, so they are computed here. A computational procedure to write the full expansion of the four and three real parameter class of solutions is proposed. %B Int Math Res Notices (2012) 2012 (6): 1352-1413 %I Oxford University Press %G en %U http://hdl.handle.net/1963/6093 %1 5979 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T13:30:44Z\\nNo. of bitstreams: 1\\n1010.1895v3.pdf: 424524 bytes, checksum: b558cd4e4da76831f67255b275392840 (MD5) %R 10.1093/imrn/rnr071 %0 Journal Article %J Riv. Mat. Univ. Parma %D 2012 %T Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles %A Daniela Tonon %XWe show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.

%B Riv. Mat. Univ. Parma %V 3 %P 163–175 %G eng %U https://hal.archives-ouvertes.fr/hal-00918409 %0 Thesis %D 2012 %T Some aspects of spinors – classical and noncommutative %A Giacomo Dossena %I SISSA %G en %U http://hdl.handle.net/1963/6317 %1 6218 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Giacomo Dossena (dossena@sissa.it) on 2012-11-13T11:13:08Z\\nNo. of bitstreams: 1\\nthesis.pdf: 1569621 bytes, checksum: 1ab89dce9cdc2097b3692da5a63ad82b (MD5) %0 Journal Article %J International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018 %D 2012 %T Some remarks on quantum mechanics %A Gianfausto Dell'Antonio %K Quantum mechanics %X We discuss the similarities and differences between the formalism of Hamiltonian Classical Mechanics and of Quantum Mechanics and exemplify the differences through an analysis of tracks in a cloud chamber. %B International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018 %I World Scientific Publishing %G en %U http://hdl.handle.net/1963/7018 %1 7013 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:45:49Z No. of bitstreams: 0 %R 10.1142/S0219887812600183 %0 Journal Article %J J. Stat. Phys. %D 2012 %T Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes %A Marco Bertola %A Buckingham, R. %A Lee, S. Y. %A Pierce, V. %B J. Stat. Phys. %V 146 %P 475–518 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2 %R 10.1007/s10955-011-0409-2 %0 Journal Article %J Rev. Math. Phys. 24 (2012), 1250017 %D 2012 %T Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions %A Michele Correggi %A Gianfausto Dell'Antonio %A Domenico Finco %A Alessandro Michelangeli %A Alessandro Teta %X We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs. %B Rev. Math. Phys. 24 (2012), 1250017 %I World Scientific %G en %U http://hdl.handle.net/1963/6069 %1 5955 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-02T07:19:59Z\\nNo. of bitstreams: 1\\n1201.5740v1.pdf: 303047 bytes, checksum: eb2df0afd547514c235422e82f494584 (MD5) %R 10.1142/S0129055X12500171 %0 Conference Paper %B 17th Int. Conf. Ships Shipp. Res. %D 2012 %T A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %B 17th Int. Conf. Ships Shipp. Res. %G eng %0 Journal Article %J Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 %D 2012 %T Sub-Riemannian structures on 3D Lie groups %A Andrei A. Agrachev %A Davide Barilari %XWe give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

%B Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 %I SISSA %G en %U http://hdl.handle.net/1963/6453 %1 6397 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T13:48:29Z\r\nNo. of bitstreams: 1\r\n1007.4970v2.pdf: 453953 bytes, checksum: 4330325299743bad4afe9f1ac7121e21 (MD5) %R 10.1007/s10883-012-9133-8 %0 Journal Article %J Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660 %D 2012 %T Systems of Quadratic Inequalities %A Andrei A. Agrachev %A Antonio Lerario %X We present a spectral sequence which efficiently computes Betti numbers of a closed semi-algebraic subset of RP^n defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in RP^n. We do not restrict ourselves to the term E_2 of the spectral sequence and give a simple explicit formula for the differential d_2. %B Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660 %I SISSA %G en %U http://hdl.handle.net/1963/7072 %1 7066 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-09-16T10:02:51Z No. of bitstreams: 1 1012.5731v2.pdf: 367584 bytes, checksum: 136c7bc2abeeb2a239c15689929eae30 (MD5) %R DOI: 10.1112/plms/pds010 %0 Journal Article %J Arch. Rational Mech. Anal. 200 (2011) 1003-1021 %D 2011 %T SBV regularity for Hamilton-Jacobi equations in R^n %A Stefano Bianchini %A Camillo De Lellis %A Roger Robyr %XIn this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

%B Arch. Rational Mech. Anal. 200 (2011) 1003-1021 %I Springer %G en %U http://hdl.handle.net/1963/4911 %1 4695 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T10:18:41Z\\nNo. of bitstreams: 1\\n1002.4087v1.pdf: 272486 bytes, checksum: 551dab603b0252ec9c22800b33360d02 (MD5) %R 10.1007/s00205-010-0381-z %0 Journal Article %J Advances in Mathematics 226 (2011) 3655-3676 %D 2011 %T Semistable and numerically effective principal (Higgs) bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %X We study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian–Yang–Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles. %B Advances in Mathematics 226 (2011) 3655-3676 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3638 %1 666 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-18T12:30:35Z\\r\\nNo. of bitstreams: 1\\r\\nBruzzo_Otero.pdf: 270209 bytes, checksum: 843961bd72149ca85c9b100395b70ed1 (MD5) %R 10.1016/j.aim.2010.10.026 %0 Journal Article %J Indiana Univ. Math. J. 60 (2011) 367-409 %D 2011 %T Singular perturbation models in phase transitions for second order materials %A Milena Chermisi %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %X A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained. %B Indiana Univ. Math. J. 60 (2011) 367-409 %I Indiana University %G en_US %U http://hdl.handle.net/1963/3858 %1 851 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:47:12Z\\r\\nNo. of bitstreams: 1\\r\\nCheDMaFonLeo_2010.pdf: 350746 bytes, checksum: b384a4d0b82dd9713e1849ad3ef6a2be (MD5) %R 10.1512/iumj.2011.60.4346 %0 Book Section %B Painlevé equations and related topics : proceedings of the international conference, Saint Petersburg, Russia, June 17-23, 2011 / Aleksandr Dmitrievich Briuno; Alexander B Batkhin. - Berlin : De Gruyter, [2012]. - p. 101-105 %D 2011 %T Solving PVI by Isomonodromy Deformations %A Davide Guzzetti %K Painlevé Equations %X The critical and asymptotic behaviors of solutions of the sixth Painlev\\\'e\r\nequation, an their parametrization in terms of monodromy data, are\r\nsynthetically reviewed. The explicit formulas are given. This paper has been\r\nwithdrawn by the author himself, because some improvements are necessary.\r\nThis is a proceedings of the international conference \"Painlevé Equations and Related Topics\" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the SteklovInstitute of Mathematicsof theRussian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011. %B Painlevé equations and related topics : proceedings of the international conference, Saint Petersburg, Russia, June 17-23, 2011 / Aleksandr Dmitrievich Briuno; Alexander B Batkhin. - Berlin : De Gruyter, [2012]. - p. 101-105 %I SISSA %@ 9783110275582 %G en %U http://hdl.handle.net/1963/6522 %1 6472 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:34:39Z\nNo. of bitstreams: 1\n17-StPeterburg12.pdf: 53422 bytes, checksum: a79d3d4bf7aa7e55c929d66671e31dfe (MD5) %0 Journal Article %J Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251 %D 2011 %T On the Space of Symmetric Operators with Multiple Ground States %A Andrei A. Agrachev %K Multiple eigenvalue %X We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite dimensional generalizations are easily guessed. %B Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251 %I SISSA %G en %U http://hdl.handle.net/1963/7069 %1 6392 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-09-16T09:28:52Z No. of bitstreams: 1 1107.3010v2.pdf: 187825 bytes, checksum: 3e6e04aeadc87e130c87ada77fe862a1 (MD5) %R DOI: 10.1007/s10688-011-0026-5 %0 Journal Article %J Journal of Dynamical and Control Systems %D 2011 %T The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry %A Bernard Bonnard %A Grégoire Charlot %A Roberta Ghezzi %A Gabriel Janin %XWe study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

%B Journal of Dynamical and Control Systems %I Springer %V 17 %P 141-161 %G en %U http://hdl.handle.net/1963/4914 %1 4692 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-25T09:38:15Z\\nNo. of bitstreams: 1\\n1009.2612v1.pdf: 263401 bytes, checksum: 0ddf4bcfd9663ee3c0da870233d119bb (MD5) %R 10.1007/s10883-011-9113-4 %0 Report %D 2011 %T Structure of level sets and Sard-type properties of Lipschitz maps %A Giovanni Alberti %A Stefano Bianchini %A Gianluca Crippa %I SISSA %G en %U http://hdl.handle.net/1963/4657 %1 4424 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-10T12:07:33Z\\nNo. of bitstreams: 1\\nAlberti_Bianchini_Crippa_51_M.pdf: 361735 bytes, checksum: b3f27bce1ab515dca94a6ad93d822160 (MD5) %0 Journal Article %J Advanced Nonlinear Studies %D 2011 %T Subharmonic solutions of planar Hamiltonian systems: a rotation number approach %A Alberto Boscaggin %B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 11 %P 77–103 %G eng %R 10.1515/ans-2011-0104 %0 Journal Article %J Le Matematiche %D 2011 %T Subharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem %A Alberto Boscaggin %XWe revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous) planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.

%B Le Matematiche %V 66 %P 115–122 %G eng %0 Journal Article %J Int Math Res Notices (2011) 2011 (24): 5625-5643 %D 2011 %T Supercritical conformal metrics on surfaces with conical singularities %A Mauro Bardelloni %A Francesca De Marchis %A Andrea Malchiodi %XWe study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

%B Int Math Res Notices (2011) 2011 (24): 5625-5643 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/4095 %1 309 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-26T07:12:29Z\\r\\nNo. of bitstreams: 1\\r\\nBarDemMal-56M.pdf: 317906 bytes, checksum: 6b2dc3222c15d6690b75440300fa4aed (MD5) %R 10.1093/imrn/rnq285 %0 Journal Article %J Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14 %D 2011 %T A system-level approach for deciphering the transcriptional response to prion infection %A Mattia Zampieri %A Giuseppe Legname %A Daniel Segrè %A Claudio Altafini %X MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. %B Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14 %I Oxford University Press %G en %U http://hdl.handle.net/1963/5745 %1 5600 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-04-23T08:12:17Z\\nNo. of bitstreams: 1\\nZaLeSeAl11.pdf: 1229345 bytes, checksum: eb5500741d42ed30ef38112ebd4eae91 (MD5) %R 10.1093/bioinformatics/btr580 %0 Journal Article %J Adv. Differential Equations %D 2010 %T Semiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential %A Alessandro Selvitella %B Adv. Differential Equations %I Khayyam Publishing, Inc. %V 15 %P 315–348 %8 03 %G eng %U https://projecteuclid.org:443/euclid.ade/1355854752 %0 Journal Article %J Geom. Dedicata 146 (2010) 27-41 %D 2010 %T On semistable principal bundles over complex projective manifolds, II %A Indranil Biswas %A Ugo Bruzzo %X Let (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero. %B Geom. Dedicata 146 (2010) 27-41 %G en_US %U http://hdl.handle.net/1963/3404 %1 928 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-31T11:15:29Z\\nNo. of bitstreams: 1\\nbiswas-bruzzo-2.pdf: 216946 bytes, checksum: 21a4d096140b009d34e486648fe1a555 (MD5) %R 10.1007/s10711-009-9424-8 %0 Report %D 2010 %T Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials %A Mouhamed Moustapha Fall %A Roberta Musina %X In this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results. %G en_US %U http://hdl.handle.net/1963/3869 %1 840 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-05-28T10:38:12Z\\nNo. of bitstreams: 1\\nFall_Musina_2010.pdf: 232933 bytes, checksum: cfcad2e3f6d3120912888f823d290d5c (MD5) %0 Journal Article %J Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 %D 2010 %T Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity %A Marta Lewicka %A Maria Giovanna Mora %A Mohammad Reza Pakzad %X We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates. %B Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295 %G en_US %U http://hdl.handle.net/1963/2601 %1 1521 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-03-11T11:36:01Z\\nNo. of bitstreams: 1\\nLewMorPak08.pdf: 342797 bytes, checksum: 4293029876d53186e1ecce89c98e5c0c (MD5) %R 10.2422/2036-2145.2010.2.02 %0 Journal Article %J Archive for Rational Mechanics and Analysis %D 2010 %T Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions %A Massimiliano Berti %A Philippe Bolle %X We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". © Springer-Verlag (2009). %B Archive for Rational Mechanics and Analysis %V 195 %P 609-642 %G eng %R 10.1007/s00205-008-0211-8 %0 Journal Article %J SIAM J. Math. Anal. 42 (2010) 2132-2154 %D 2010 %T Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit %A Tamara Grava %A Tom Claeys %X We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation. %B SIAM J. Math. Anal. 42 (2010) 2132-2154 %G en_US %U http://hdl.handle.net/1963/3839 %1 488 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-05T10:12:44Z\\nNo. of bitstreams: 1\\n0911.5686v1.pdf: 311708 bytes, checksum: bfe41688febbfb066ebaae202e1e93b6 (MD5) %R 10.1137/090779103 %0 Journal Article %J Inverse Problems %D 2010 %T Stable determination of an immersed body in a stationary Stokes fluid %A Andrea Ballerini %XWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log–log type.

%B Inverse Problems %I IOP Publishing %V 26 %P 125015 %8 nov %G eng %U https://doi.org/10.1088%2F0266-5611%2F26%2F12%2F125015 %R 10.1088/0266-5611/26/12/125015 %0 Journal Article %J J. Math. Anal. Appl. 352 (2009) 99-111 %D 2009 %T On a Sobolev type inequality related to the weighted p-Laplace operator %A Marita Gazzini %A Roberta Musina %B J. Math. Anal. Appl. 352 (2009) 99-111 %G en_US %U http://hdl.handle.net/1963/2613 %1 1510 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-03T10:13:10Z\\nNo. of bitstreams: 1\\nGaMu3.pdf: 298467 bytes, checksum: 6de8ed2f5202430d4c5b002c5f613347 (MD5) %R 10.1016/j.jmaa.2008.06.021 %0 Journal Article %J Mathematical Models and Methods in Applied Sciences %D 2009 %T Solutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions %A Ianni, Isabella %A Giusi Vaira %XIn this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

%B Mathematical Models and Methods in Applied Sciences %V 19 %P 707-720 %G eng %U https://doi.org/10.1142/S0218202509003589 %R 10.1142/S0218202509003589 %0 Journal Article %J Adv. Math. 221 (2009) 1843-1909 %D 2009 %T Some new entire solutions of semilinear elliptic equations on Rn %A Andrea Malchiodi %B Adv. Math. 221 (2009) 1843-1909 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3645 %1 659 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-08T15:11:59Z\\nNo. of bitstreams: 1\\nentire.pdf: 478191 bytes, checksum: 1b7ea59917a621bf7b2793f7228fade6 (MD5) %R 10.1016/j.aim.2009.03.012 %0 Journal Article %J Math. Models Methods Appl. Sci. 19 (2009) 601-630 %D 2009 %T Strain-order coupling in nematic elastomers: equilibrium configurations %A Pierluigi Cesana %A Antonio DeSimone %X We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations. %B Math. Models Methods Appl. Sci. 19 (2009) 601-630 %G en_US %U http://hdl.handle.net/1963/2700 %1 1400 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-25T15:04:59Z\\nNo. of bitstreams: 1\\nprprCdS.pdf: 504721 bytes, checksum: 2ef9aff006dbc9353a50a122cb98d381 (MD5) %0 Report %D 2009 %T Stratos: a code for 3D free surface flows with floating constraints %A Antonio DeSimone %A B. Bianchi %A Luca Heltai %X This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers...... %G en_US %U http://hdl.handle.net/1963/3701 %1 604 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:37:01Z\\nNo. of bitstreams: 1\\nBianchiDeSimoneHeltai.pdf: 899803 bytes, checksum: aff44eb1a39c6fd4acd4b3cb285e2d64 (MD5) %0 Journal Article %J Calc. Var. Partial Differential Equations 33 (2008) 37-74 %D 2008 %T A second order minimality condition for the Mumford-Shah functional %A Filippo Cagnetti %A Maria Giovanna Mora %A Massimiliano Morini %X A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given. %B Calc. Var. Partial Differential Equations 33 (2008) 37-74 %G en_US %U http://hdl.handle.net/1963/1955 %1 2318 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-03-02T12:54:00Z\\nNo. of bitstreams: 1\\nCMM.pdf: 358759 bytes, checksum: c414c0080a17971ecba1251a5890b94f (MD5) %R 10.1007/s00526-007-0152-3 %0 Journal Article %J Int. Math. Res. Not. vol. 2008, article ID rnn035 %D 2008 %T On semistable principal bundles over a complex projective manifold %A Indranil Biswas %A Ugo Bruzzo %X Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface. %B Int. Math. Res. Not. vol. 2008, article ID rnn035 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3418 %1 917 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T09:53:34Z\\nNo. of bitstreams: 1\\n0803.4042v1.pdf: 273878 bytes, checksum: 8f729aa65d9cebf234016c17cacfedbc (MD5) %R 10.1093/imrn/rnn035 %0 Journal Article %J J. Funct. Anal. 254 (2008) 2816-2845 %D 2008 %T Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn %A Antonio Ambrosetti %A Giovanna Cerami %A David Ruiz %X Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations. %B J. Funct. Anal. 254 (2008) 2816-2845 %G en_US %U http://hdl.handle.net/1963/2175 %1 2069 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T08:29:15Z\\nNo. of bitstreams: 1\\nambceruiz.pdf: 305881 bytes, checksum: f00a4a8078e5c5d78d4309cceb317906 (MD5) %R 10.1016/j.jfa.2007.11.013 %0 Journal Article %J Commun. Pure Appl. Anal. 7 (2008) 1-21 %D 2008 %T Stability of planar switched systems: the nondiagonalizable case %A Ugo Boscain %A Moussa Balde %B Commun. Pure Appl. Anal. 7 (2008) 1-21 %G en_US %U http://hdl.handle.net/1963/1857 %1 2361 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-09-28T09:15:19Z\\nNo. of bitstreams: 1\\n44-M.pdf: 3158552 bytes, checksum: c4fee14d81a9fcf026efd4448da88c75 (MD5) %R 10.3934/cpaa.2008.7.1 %0 Journal Article %J Algebra Number Theory 2 (2008) 313-345 %D 2008 %T Symmetric obstruction theories and Hilbert schemes of points on threefolds %A Kai Behrend %A Barbara Fantechi %X In an earlier paper by one of us (Behrend), Donaldson-Thomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical\\nZ-valued constructible function on the moduli space. This constructible function associates to\\nany point of the moduli space a certain invariant of the singularity of the space at the point. Here we evaluate this invariant for the case of a singularity that is an isolated point of a C∗-action and that admits a symmetric obstruction theory compatible with the C∗-action. The answer is (-1)d, where d\\nis the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the Donaldson-Thomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande. %B Algebra Number Theory 2 (2008) 313-345 %G en_US %U http://hdl.handle.net/1963/2709 %1 1392 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-22T08:20:28Z\\nNo. of bitstreams: 1\\n0512556v1.pdf: 377619 bytes, checksum: ba4796d5d4103e23a359d4fe4d01ca2f (MD5) %0 Thesis %D 2008 %T Symmetries of noncommutative spaces and equivariant cohomology %A Lucio Cirio %K Noncommutative spaces %X As the title suggests, the main subject of this thesis is the study of symmetries of noncommutative spaces and related equivariant cohomologies. We focus on deformations of classical geometries coming from the action of some symmetry. A close relation between the deformation of the symmetry and the deformation of the space on which it acts is at the heart of our approach; we will use this idea to generate noncommutative geometries, and to de¯ne algebraic models for the equivariant cohomology of such actions. %I SISSA %G en %U http://hdl.handle.net/1963/5254 %1 5077 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-01-23T08:57:48Z\\nNo. of bitstreams: 1\\nPhD_Cirio.pdf: 579480 bytes, checksum: 59e7b02846b913cd48e3c84e1e9a2bea (MD5) %0 Report %D 2007 %T Semistable principal Higgs bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %G en_US %U http://hdl.handle.net/1963/2533 %1 1585 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-17T09:52:22Z\\nNo. of bitstreams: 1\\nPrincHiggs-2.pdf: 197562 bytes, checksum: 44797463786b3c14408f7d1898531202 (MD5) %0 Report %D 2007 %T Smooth toric DM stacks %A Barbara Fantechi %A Etienne Mann %A Fabio Nironi %X We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks. %G en_US %U http://hdl.handle.net/1963/2120 %1 2123 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T06:41:10Z\\nNo. of bitstreams: 1\\ntoricarxiv.pdf: 426672 bytes, checksum: e73e63b89023046b5d53b7f7f6c2e580 (MD5) %0 Report %D 2007 %T Soft elasticity and microstructure in smectic C elastomers %A Antonio DeSimone %A James Adams %A Sergio Conti %X Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable. %B Contin. Mech. Thermodyn. 18 (2007) 319-334 %G en_US %U http://hdl.handle.net/1963/1811 %1 2403 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-12T09:42:24Z\\nNo. of bitstreams: 1\\nsissa05M-06.pdf: 394760 bytes, checksum: 95c4183d6cb1210bf2a689ae083a3cb7 (MD5) %R 10.1007/s00161-006-0031-8 %0 Journal Article %J J. Math. Anal. Appl. 335 (2007) 1143-1160 %D 2007 %T Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals %A Sandro Zagatti %X We provide a unified approach to prove existence results for the Dirichlet problem for Hamilton-Jacobi equations and for the minimum problem for nonquasiconvex functionals of the Calculus of Variations with affine boundary data. The idea relies on the definition of integro-extremal solutions introduced in the study of nonconvex scalar variational problem. %B J. Math. Anal. Appl. 335 (2007) 1143-1160 %G en_US %U http://hdl.handle.net/1963/2763 %1 1937 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T11:05:58Z\\nNo. of bitstreams: 1\\nhjcvjmaa2.pdf: 158429 bytes, checksum: 712208cb11d8543ac2f9f5f01956dcfe (MD5) %R 10.1016/j.jmaa.2007.02.034 %0 Report %D 2007 %T Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result %A Fethi Mahmoudi %A Andrea Malchiodi %X We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result. %G en_US %U http://hdl.handle.net/1963/2111 %1 2578 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-17T08:58:17Z\\nNo. of bitstreams: 1\\n0708.0104v1.pdf: 663755 bytes, checksum: bbc4a382b0338288fa6ce9002872d955 (MD5) %0 Report %D 2007 %T Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions %A Fethi Mahmoudi %A Andrea Malchiodi %A Marcelo Montenegro %X We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part. %G en_US %U http://hdl.handle.net/1963/2112 %1 2577 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-17T09:14:27Z\\nNo. of bitstreams: 1\\n0708.0125v1.pdf: 498331 bytes, checksum: 95036be8fb1f07136be4d6bdc1aab642 (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 %D 2007 %T Some existence results for the Toda system on closed surfaces %A Andrea Malchiodi %A Cheikh Birahim Ndiaye %X Given a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412 %G en_US %U http://hdl.handle.net/1963/1775 %1 2769 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-29T08:29:06Z\\nNo. of bitstreams: 1\\n75M.pdf: 258110 bytes, checksum: 18821ff73b71e5079c15c32f59961ad9 (MD5) %R 10.4171/RLM/504 %0 Journal Article %J NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 %D 2007 %T Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws %A Andrea Marson %A Carlotta Donadello %B NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592 %G en_US %U http://hdl.handle.net/1963/1769 %1 2775 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-28T10:29:02Z\\nNo. of bitstreams: 1\\n68M.pdf: 209186 bytes, checksum: 79dcb94eb1405cbadb411592b2cffe66 (MD5) %R 10.1007/s00030-007-5010-7 %0 Report %D 2007 %T Standing waves of some coupled Nonlinear Schrödinger Equations %A Antonio Ambrosetti %A Eduardo Colorado %X We deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large. %B J. Lond. Math. Soc. 75 (2007) 67-82 %G en_US %U http://hdl.handle.net/1963/1821 %1 2393 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-18T14:55:22Z\\nNo. of bitstreams: 1\\nsissa,2_2006_M.pdf: 431407 bytes, checksum: 0e294e77a4423c4b41ce178df2187dd3 (MD5) %R 10.1112/jlms/jdl020 %0 Report %D 2007 %T Strengthened convergence of marginals to the cubic nonlinear Schroedinger equation %A Alessandro Michelangeli %X We rewrite a recent derivation of the cubic non-linear Schroedinger equation by Adami, Golse, and Teta in the more natural formof the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the\\nnon-linear effective dynamics of a large system of interacting bosons is\\nproved in the literature. %G en_US %U http://hdl.handle.net/1963/1977 %1 2218 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-06-06T09:21:56Z\\nNo. of bitstreams: 1\\nstrengthened.pdf: 228368 bytes, checksum: c87b1b3ae8fd722412cf906c5f44df5b (MD5) %0 Journal Article %J Arch. Rational Mech. Anal. 183 (2007) 411-456 %D 2007 %T Surfactants in Foam Stability: A Phase-Field Model %A Irene Fonseca %A Massimiliano Morini %A Valeriy Slastikov %X The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation. %B Arch. Rational Mech. Anal. 183 (2007) 411-456 %G en_US %U http://hdl.handle.net/1963/2035 %1 2161 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T15:51:40Z\\nNo. of bitstreams: 1\\n05-CNA-012.pdf: 414998 bytes, checksum: 3c44841388edba53080d531beadad798 (MD5) %R 10.1007/s00205-006-0012-x %0 Journal Article %J Comm. Math. Phys. %D 2006 %T Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions %A Marco Bertola %A B. Eynard %A Harnad, J. %B Comm. Math. Phys. %V 263 %P 401–437 %G eng %0 Journal Article %J Differential Geom. Appl. 24 (2006) 403-416 %D 2006 %T Semistability vs. nefness for (Higgs) vector bundles %A Ugo Bruzzo %A Daniel Hernandez Ruiperez %X According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E. %B Differential Geom. Appl. 24 (2006) 403-416 %G en_US %U http://hdl.handle.net/1963/2237 %1 2007 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-16T09:06:35Z\\nNo. of bitstreams: 1\\n0310040v3.pdf: 216788 bytes, checksum: 574f5aac93686c2348a6313bd129cb61 (MD5) %R 10.1016/j.difgeo.2005.12.007 %0 Report %D 2006 %T On Separation of Variables for Homogeneous SL(r) Gaudin Systems %A Gregorio Falqui %A Fabio Musso %X By means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case. %B Math. Phys. Anal. Geom. 9 (2006), n. 3, 233-262 (2007) %G en_US %U http://hdl.handle.net/1963/2538 %1 1581 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-19T11:26:08Z\\nNo. of bitstreams: 1\\n0402026v1.pdf: 312976 bytes, checksum: e99c241d72908de5b5bf69b0a7dd1c5c (MD5) %R 10.1007/s11040-006-9012-1 %0 Journal Article %J J. Math. Phys. 47 (2006) 062105 %D 2006 %T Spectral geometry of k-Minkowski space %A Francesco D'Andrea %XAfter recalling Snyder's idea of using vector fields over a smooth manifold as "coordinates on a noncommutative space", we discuss a two dimensional toy-model whose "dual" noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its "spectral properties" and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.

%B J. Math. Phys. 47 (2006) 062105 %G en_US %U http://hdl.handle.net/1963/2131 %1 2112 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T11:48:16Z\\nNo. of bitstreams: 1\\n0503012v4.pdf: 270606 bytes, checksum: b96bcb17609481fbf7d542681a2c0cfa (MD5) %R 10.1063/1.2204808 %0 Report %D 2006 %T Stability of planar nonlinear switched systems %A Ugo Boscain %A Grégoire Charlot %A Mario Sigalotti %X We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields. %B Discrete Contin. Dyn. Syst. 15 (2006) 415-432 %G en_US %U http://hdl.handle.net/1963/1710 %1 2441 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T08:35:31Z\\nNo. of bitstreams: 1\\nmath.OC0502361.pdf: 322404 bytes, checksum: e56f0d709d97e2e300e3cb9d4a629a1b (MD5) %0 Journal Article %J Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %D 2005 %T Self-similar folding patterns and energy scaling in compressed elastic sheets %A Sergio Conti %A Antonio DeSimone %A Stefan Müller %X Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves. %B Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3000 %1 1333 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:37:14Z\\nNo. of bitstreams: 1\\npreprint2004_3.pdf: 907333 bytes, checksum: 2b22c209b91ba2ddacc1a1c14a9054a2 (MD5) %R 10.1016/j.cma.2004.07.044 %0 Book Section %B Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 %D 2005 %T A short introduction to optimal control %A Ugo Boscain %A Benedetto Piccoli %B Contrôle non linéaire et applications: Cours donnés à l\\\'école d\\\'été du Cimpa de l\\\'Université de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005 %@ 2 7056 6511 0 %G en_US %U http://hdl.handle.net/1963/2257 %1 1990 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:30:24Z\\nNo. of bitstreams: 1\\nNotes-OptCont.pdf: 442775 bytes, checksum: 196e4d9cc52950dd18cf17feb0e89808 (MD5) %0 Generic %D 2005 %T Solutions of Neumann problems in domains with cracks and applications to fracture mechanics %A Gianni Dal Maso %G en_US %U http://hdl.handle.net/1963/1684 %1 79 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-05-20T07:18:38Z\\nNo. of bitstreams: 1\\nmath.AP0105132.pdf: 225826 bytes, checksum: d7308b70020a416522235ed54b404379 (MD5) %0 Journal Article %J C. R. Math. 340 (2005) 819-822 %D 2005 %T The spectral geometry of the equatorial Podles sphere %A Ludwik Dabrowski %A Giovanni Landi %A Mario Paschke %A Andrzej Sitarz %X We propose a slight modification of the properties of a spectral geometry a la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podles sphere we construct suq2-equivariant Dirac operator and real structure which satisfy these modified properties. %B C. R. Math. 340 (2005) 819-822 %G en_US %U http://hdl.handle.net/1963/2275 %1 1972 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-22T09:37:10Z\\nNo. of bitstreams: 1\\n0408034v2.pdf: 95565 bytes, checksum: 1c0e7836d4006a796eb943f128938773 (MD5) %R 10.1016/j.crma.2005.04.003 %0 Journal Article %J J. Math. Anal. Appl. 308 (2005) 221-239 %D 2005 %T Stability of solutions of quasilinear parabolic equations %A Giuseppe Maria Coclite %A Helge Holden %X We bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth. %B J. Math. Anal. Appl. 308 (2005) 221-239 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2892 %1 1808 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T12:48:15Z\\nNo. of bitstreams: 1\\n0306160v1.pdf: 240791 bytes, checksum: 4654ca0f7a1735bc7ee6666d37a2d57a (MD5) %R 10.1016/j.jmaa.2005.01.026 %0 Journal Article %J Int. J. Numer. Anal. Met. 29 (2005) 73-101 %D 2005 %T Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains %A Antonio DeSimone %A Claudio Tamagnini %X Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. %B Int. J. Numer. Anal. Met. 29 (2005) 73-101 %G en_US %U http://hdl.handle.net/1963/2165 %1 2079 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T12:02:04Z\\nNo. of bitstreams: 1\\nDeSimoneTamagnini_2005.pdf: 1179767 bytes, checksum: 23b892b2314ea8e2199cc2b2449386b0 (MD5) %R 10.1002/nag.405 %0 Journal Article %J J. Phys. A 37 (2004) 5605-5624 %D 2004 %T Semiclassical analysis of constrained quantum systems %A Gianfausto Dell'Antonio %A Lucattilio Tenuta %X We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar^(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system. %B J. Phys. A 37 (2004) 5605-5624 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/2997 %1 1336 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T08:52:42Z\\nNo. of bitstreams: 1\\n0312034v2.pdf: 270295 bytes, checksum: ade82e7ba05cc6dbf50709fd277e1323 (MD5) %R 10.1088/0305-4470/37/21/007 %0 Journal Article %J Internat. J. Game Theory 32 (2004) 561-593 %D 2004 %T Semi-cooperative strategies for differential games %A Alberto Bressan %A Wen Shen %X The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic. %B Internat. J. Game Theory 32 (2004) 561-593 %I Springer %G en_US %U http://hdl.handle.net/1963/2893 %1 1807 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T08:11:56Z\\nNo. of bitstreams: 1\\n069.pdf: 389569 bytes, checksum: 3cea0d9a5adfd0be673a7d69218e238a (MD5) %R 10.1007/s001820400180 %0 Journal Article %J SIAM J. Math. Anal. 36 (2004) 659-677 %D 2004 %T A sharp decay estimate for positive nonlinear waves %A Alberto Bressan %A Tong Yang %X We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers\\\' equation with impulsive sources. %B SIAM J. Math. Anal. 36 (2004) 659-677 %I SIAM %G en_US %U http://hdl.handle.net/1963/2916 %1 1784 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:37:38Z\\nNo. of bitstreams: 1\\nmath.AP0307140.pdf: 167236 bytes, checksum: 9e7a6fecd3de67843ca5c73f13bd841d (MD5) %R 10.1137/S0036141003427774 %0 Journal Article %J Int. Math. Res. Not. 2004, no. 32, 1619-1683 %D 2004 %T Singular Z_N curves, Riemann-Hilbert problem and modular solutions of the Schlesinger equation %A Victor Z. Enolski %A Tamara Grava %X We are solving the classical Riemann-Hilbert problem of rank N>1 on the extended complex plane punctured in 2m+2 points, for NxN quasi-permutation monodromy matrices. Following Korotkin we solve the Riemann-Hilbert problem in terms of the Szego kernel of certain Riemann surfaces branched over the given 2m+2 points. These Riemann surfaces are constructed from a permutation representation of the symmetric group S_N to which the quasi-permutation monodromy representation has been reduced. The permutation representation of our problem generates the cyclic subgroup Z_N. For this reason the corresponding Riemann surfaces of genus N(m-1) have Z_N symmetry. This fact enables us to write the matrix entries of the solution of the NxN Riemann-Hilbert problem as a product of an algebraic function and theta-function quotients. The algebraic function turns out to be related to the Szego kernel with zero characteristics. From the solution of the Riemann- Hilbert problem we automatically obtain a particular solution of the Schlesinger system. The tau-function of the Schlesinger system is computed explicitly. The rank 3 problem with four singular points (0,t,1,\\\\infty) is studied in detail. The corresponding solution of the Riemann-Hilbert problem and the Schlesinger system is given in terms of Jacobi\\\'s theta-function with modulus T=T(t), Im(T)>0. The function T=T(t) is invertible if it belongs to the Siegel upper half space modulo the subgroup \\\\Gamma_0(3) of the modular group. The inverse function t=t(T) generates a solution of a general Halphen system. %B Int. Math. Res. Not. 2004, no. 32, 1619-1683 %G en_US %U http://hdl.handle.net/1963/2540 %1 1579 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T10:08:03Z\\nNo. of bitstreams: 1\\n0306050v2.pdf: 587970 bytes, checksum: 3d350364af41be2317176944f1d85868 (MD5) %R 10.1155/S1073792804132625 %0 Journal Article %J Indiana Univ. Math. J. 53 (2004) 297-392 %D 2004 %T Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %B Indiana Univ. Math. J. 53 (2004) 297-392 %I Indiana University Mathematics Journal %G en %U http://hdl.handle.net/1963/1663 %1 2455 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:06:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1512/iumj.2004.53.2400 %0 Journal Article %J SIAM J. Control Optim. 43 (2004) 194-215 %D 2004 %T Small BV solutions of hyperbolic noncooperative differential games %A Alberto Bressan %A Wen Shen %X The paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game. %B SIAM J. Control Optim. 43 (2004) 194-215 %I SIAM %G en_US %U http://hdl.handle.net/1963/2917 %1 1783 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:46:04Z\\nNo. of bitstreams: 1\\n021.pdf: 296267 bytes, checksum: 16f3c148f2a00551188fee22ac90f666 (MD5) %R 10.1137/S0363012903425581 %0 Journal Article %J Electron. J. Differential Equations (2004) 94 %D 2004 %T Solitary waves for Maxwell Schrodinger equations %A Giuseppe Maria Coclite %A Vladimir Georgiev %X In this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated. %B Electron. J. Differential Equations (2004) 94 %I SISSA Library %G en %U http://hdl.handle.net/1963/1582 %1 2536 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:52Z (GMT). No. of bitstreams: 1\\nmath.AP0303142.pdf: 326987 bytes, checksum: 37c172f10800ae7a41e5398f6a0a0a0e (MD5)\\n Previous issue date: 2002 %0 Journal Article %J C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 %D 2004 %T Solutions concentrating at curves for some singularly perturbed elliptic problems %A Andrea Malchiodi %B C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780 %I Elsevier %G en %U http://hdl.handle.net/1963/4869 %1 4647 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T14:23:50Z\\nNo. of bitstreams: 0 %R 10.1016/j.crma.2004.03.023 %0 Journal Article %J Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661 %D 2004 %T Soluzioni periodiche di PDEs Hamiltoniane %A Massimiliano Berti %B Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661 %I Unione Matematica Italiana %G en %U http://hdl.handle.net/1963/4582 %1 4351 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-07T10:33:48Z\\nNo. of bitstreams: 1\\nberti2004.pdf: 249023 bytes, checksum: bab6b2d956c1de46de694dfca3bc4cec (MD5) %0 Journal Article %J Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233 %D 2004 %T Some remarks on multidimensional systems of conservation laws %A Alberto Bressan %X This note is concerned with the Cauchy problem for hyperbolic systems of conservation\\nlaws in several space dimensions. We first discuss an example of ill-posedness, for a special system\\nhaving a radial symmetry property. Some conjectures are formulated, on the compactness of the set of\\nflow maps generated by vector fields with bounded variation. %B Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233 %I Accademia Nazionale dei Lincei %G en_US %U http://hdl.handle.net/1963/3642 %1 662 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-21T10:01:16Z\\nNo. of bitstreams: 1\\nM2004-34-21.pdf: 187400 bytes, checksum: 045bd5d68458b90865a3a4c132a90163 (MD5) %0 Journal Article %J ESAIM COCV 10 (2004) 168-200 %D 2004 %T Stability rates for patchy vector fields %A Fabio Ancona %A Alberto Bressan %X This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term. %B ESAIM COCV 10 (2004) 168-200 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2959 %1 1741 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-22T08:49:39Z\\nNo. of bitstreams: 1\\n0111109v1.pdf: 336899 bytes, checksum: 851fc204f3e9f254b9122e0bd1f8894f (MD5) %R 10.1051/cocv:2004003 %0 Journal Article %J Nucl. Phys. B 678 (2004) 638-655 %D 2004 %T Superlocalization formulas and supersymmetric Yang-Mills theories %A Ugo Bruzzo %A Francesco Fucito %X By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions. %B Nucl. Phys. B 678 (2004) 638-655 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2886 %1 1814 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T10:17:55Z\\nNo. of bitstreams: 1\\n0310036v1.pdf: 236322 bytes, checksum: 97623018f9c2507ac14381b6a288c53d (MD5) %R 10.1016/j.nuclphysb.2003.11.033 %0 Journal Article %J J. High Energy Phys. %D 2003 %T Second and third order observables of the two-matrix model %A Marco Bertola %B J. High Energy Phys. %P 062, 30 pp. (electronic) %G eng %0 Journal Article %J Math. Phys. Anal. Geom. 6 (2003) 139-179 %D 2003 %T Separation of variables for Bi-Hamiltonian systems %A Gregorio Falqui %A Marco Pedroni %X We address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations. %B Math. Phys. Anal. Geom. 6 (2003) 139-179 %I SISSA Library %G en %U http://hdl.handle.net/1963/1598 %1 2520 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:05:06Z (GMT). No. of bitstreams: 1\\nnlin.SI0204029.pdf: 376655 bytes, checksum: 1bea838d34e847ea2d6e7ec8731cdb22 (MD5)\\n Previous issue date: 2002 %R 10.1023/A:1024080315471 %0 Journal Article %J SIAM J. Math. Anal. 35 (2003) 759-805 %D 2003 %T Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems %A Massimiliano Morini %X We prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown. %B SIAM J. Math. Anal. 35 (2003) 759-805 %I SIAM %G en_US %U http://hdl.handle.net/1963/3071 %1 1262 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:24:32Z\\nNo. of bitstreams: 1\\nsingper.pdf: 523839 bytes, checksum: 9d1bcc064d165e9b964422c8acd396bb (MD5) %R 10.1137/S0036141001395388 %0 Thesis %D 2003 %T Single-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem %A Mario Sigalotti %I SISSA %G en %U http://hdl.handle.net/1963/5342 %1 5170 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-02-02T12:08:29Z\\nNo. of bitstreams: 1\\nPhD_Sigalotti_Mario.pdf: 8050196 bytes, checksum: e113b00d1c0f5b37484c26f023914baa (MD5) %0 Journal Article %J Comm. Math. Phys. 235 (2003) no.3, 427-466 %D 2003 %T Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %B Comm. Math. Phys. 235 (2003) no.3, 427-466 %I Springer %G en %U http://hdl.handle.net/1963/1633 %1 2485 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:37Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %R 10.1007/s00220-003-0811-y %0 Journal Article %J SIAM J.Control Optim. 41 (2003),no.2, 607 %D 2003 %T Some results on the boundary control of systems of conservation laws %A Alberto Bressan %A Fabio Ancona %A Giuseppe Maria Coclite %B SIAM J.Control Optim. 41 (2003),no.2, 607 %I SISSA Library %G en %U http://hdl.handle.net/1963/1615 %1 2503 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:20Z (GMT). No. of bitstreams: 1\\nmath.AP0205246.pdf: 155904 bytes, checksum: 294663b00a9e6b6ae91096fd628a942a (MD5)\\n Previous issue date: 2002 %R 10.1137/S0363012901392529 %0 Journal Article %J Adv. Theor. Math. Phys. 7 (2003) 145-204 %D 2003 %T Space-adiabatic perturbation theory %A Gianluca Panati %A Herbert Spohn %A Stefan Teufel %X We study approximate solutions to the Schr\\\\\\\"odinger equation $i\\\\epsi\\\\partial\\\\psi_t(x)/\\\\partial t = H(x,-i\\\\epsi\\\\nabla_x) \\\\psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of bounded operators on the Hilbert space $\\\\Hi_{\\\\rm f}$ of fast ``internal\\\'\\\' degrees of freedom. By assumption $H(q,p)$ has an isolated energy band. Using a method of Nenciu and Sordoni \\\\cite{NS} we prove that interband transitions are suppressed to any order in $\\\\epsi$. As a consequence, associated to that energy band there exists a subspace of $L^2(\\\\mathbb{R}^d,\\\\Hi _{\\\\rm f})$ almost invariant under the unitary time evolution. We develop a systematic perturbation scheme for the computation of effective Hamiltonians which govern approximately the intraband time evolution. As examples for the general perturbation scheme we discuss the Dirac and Born-Oppenheimer type Hamiltonians and we reconsider also the time-adiabatic theory. %B Adv. Theor. Math. Phys. 7 (2003) 145-204 %I International Press %G en_US %U http://hdl.handle.net/1963/3041 %1 1292 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-08T12:17:36Z\\nNo. of bitstreams: 1\\n0201055v3.pdf: 449361 bytes, checksum: a37ea04fc4a4f59a75d03e4b2ec3df16 (MD5) %0 Journal Article %J J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 %D 2003 %T A stability result for nonlinear Neumann problems under boundary variations %A Gianni Dal Maso %A Francois Ebobisse %A Marcello Ponsiglione %X In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology. %B J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 %I SISSA Library %G en %U http://hdl.handle.net/1963/1618 %1 2500 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:23Z (GMT). No. of bitstreams: 1\\nmath.AP0206215.pdf: 329673 bytes, checksum: 40d537fd197fbaec56be0729d3a72ee3 (MD5)\\n Previous issue date: 2002 %R 10.1016/S0021-7824(03)00014-X %0 Journal Article %J Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445 %D 2002 %T The scalar curvature problem on $S\\\\sp n$: an approach via Morse theory %A Andrea Malchiodi %B Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445 %I Springer %G en %U http://hdl.handle.net/1963/1331 %1 3124 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:24Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1007/s005260100110 %0 Journal Article %J Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 %D 2002 %T Singular elliptic problems with critical growth %A Paolo Caldiroli %A Andrea Malchiodi %B Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 %I Dekker %G en %U http://hdl.handle.net/1963/1268 %1 3187 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:34Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1081/PDE-120004887 %0 Journal Article %J C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 %D 2002 %T Solutions concentrating on spheres to symmetric singularly perturbed problems %A Antonio Ambrosetti %A Andrea Malchiodi %A Wei-Ming Ni %X We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere. %B C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150 %I SISSA Library %G en %U http://hdl.handle.net/1963/1594 %1 2524 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:03Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 2002 %R 10.1016/S1631-073X(02)02414-7 %0 Thesis %D 2002 %T Space-adiabatic Decoupling in Quantum Dynamics %A Gianluca Panati %I SISSA %G en %U http://hdl.handle.net/1963/6360 %1 6292 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-12-21T16:35:07Z\\nNo. of bitstreams: 1\\nPhD_Panati_Gianluca.pdf: 9088755 bytes, checksum: 75624cfaef0563f1f1184f2dd0f2f955 (MD5) %0 Journal Article %J Physical review letters. 2002 Jun; 88(25 Pt 1):250405 %D 2002 %T Space-adiabatic perturbation theory in quantum dynamics %A Gianluca Panati %A Herbert Spohn %A Stefan Teufel %X A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schrödinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders, and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications, we discuss the Born-Oppenheimer theory to second order and derive for the first time the nonperturbative definition of the g factor of the electron within nonrelativistic quantum electrodynamics. %B Physical review letters. 2002 Jun; 88(25 Pt 1):250405 %I American Physical Society %G en %U http://hdl.handle.net/1963/5985 %1 5841 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Marta Maurutto (maurutto@sissa.it) on 2012-07-15T14:04:06Z\\nNo. of bitstreams: 0 %R 10.1103/PhysRevLett.88.250405 %0 Journal Article %J SIAM J. Control Optim. 41 (2002), no. 1, 89-112 %D 2002 %T Stability of planar switched systems: the linear single input case %A Ugo Boscain %X We study the stability of the origin for the dynamical system $\\\\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where A and B are two 2 × 2 real matrices with eigenvalues having strictly negative real part, $x\\\\in {\\\\mbox{{\\\\bf R}}}^2$, and $u(.):[0,\\\\infty[\\\\to[0,1]$ is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). The result is obtained without looking for a common Lyapunov function but studying the locus in which the two vector fields Ax and Bx are collinear. There are only three relevant parameters: the first depends only on the eigenvalues of A, the second depends only on the eigenvalues of B, and the third contains the interrelation among the two systems, and it is the cross ratio of the four eigenvectors of A and B in the projective line CP1. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied. %B SIAM J. Control Optim. 41 (2002), no. 1, 89-112 %I SIAM %G en %U http://hdl.handle.net/1963/1529 %1 2634 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1137/S0363012900382837 %0 Journal Article %J P. Am. Math. Soc., 2002, 130, 1961 %D 2002 %T On the Stability of the Standard Riemann Semigroup %A Stefano Bianchini %A Rinaldo M. Colombo %B P. Am. Math. Soc., 2002, 130, 1961 %I SISSA Library %G en %U http://hdl.handle.net/1963/1528 %1 2635 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:40Z (GMT). No. of bitstreams: 1\\nmath.AP0007055.pdf: 195640 bytes, checksum: 3708c7f60ae79e0790175863c0290b0e (MD5)\\n Previous issue date: 2000 %0 Book Section %B Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 %D 2001 %T S^2 type parametric surfaces with prescribed mean curvature and minimal energy %A Paolo Caldiroli %A Roberta Musina %B Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 %I Birkhauser %G en %U http://hdl.handle.net/1963/1605 %1 2513 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 %D 2001 %T On the spreading of characteristics for non-convex conservation laws %A Helge Kristian Jenssen %A Carlo Sinestrari %X We study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos\\\' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an Hölder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution. %B Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925 %I Cambridge University Press %G en_US %U http://hdl.handle.net/1963/3265 %1 1436 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-10T13:53:07Z\\nNo. of bitstreams: 1\\nJS2.pdf: 302742 bytes, checksum: 563821a822c34aef0ca1b4c55065827c (MD5) %R 10.1017/S0308210500001189 %0 Journal Article %J Siam J. Math. Anal., 2001, 33, 959 %D 2001 %T Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions %A Stefano Bianchini %X We consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and u(0,\\\\cdot) = u_0, where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates $w$, we prove that there exists a semigroup of solutions $u(t) = \\\\mathcal{S}_t u_0$, defined on initial data $u_0 \\\\in L^\\\\infty$. The semigroup $\\\\mathcal{S}$ is continuous w.r.t. time and the initial data $u_0$ in the $L^1_{\\\\text{loc}}$ topology. Moreover $\\\\mathcal{S}$ is unique and its trajectories are obtained as limits of wave front tracking approximations. %B Siam J. Math. Anal., 2001, 33, 959 %I SISSA Library %G en %U http://hdl.handle.net/1963/1523 %1 2640 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:35Z (GMT). No. of bitstreams: 1\\nmath.AP0006094.pdf: 295215 bytes, checksum: 756406a074bc2e1702b76422489572cc (MD5)\\n Previous issue date: 2000 %R 10.1137/S0036141000377900 %0 Journal Article %J Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. %D 2001 %T Stationary states for a two-dimensional singular Schrodinger equation %A Paolo Caldiroli %A Roberta Musina %B Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. %I SISSA Library %G en %U http://hdl.handle.net/1963/1249 %1 3206 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Ann. I. H. Poincare - An., 2001, 18, 359 %D 2001 %T On the subanalyticity of Carnot-Caratheodory distances %A Andrei A. Agrachev %A Jean-Paul Gauthier %B Ann. I. H. Poincare - An., 2001, 18, 359 %I SISSA Library %G en %U http://hdl.handle.net/1963/1483 %1 2680 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:03Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1016/S0294-1449(00)00064-0 %0 Journal Article %J J. Differential Equations 170 (2001) 228-245 %D 2001 %T On the symmetric scalar curvature problem on S\\\\sp n %A Antonio Ambrosetti %A Andrea Malchiodi %X We discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries. %B J. Differential Equations 170 (2001) 228-245 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3095 %1 1238 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-14T10:19:50Z\\nNo. of bitstreams: 1\\nAmbrosettiMalchiodixx.pdf: 307157 bytes, checksum: 40112a5a91f2314b5e07f647bb5fa92a (MD5) %R 10.1006/jdeq.2000.3816 %0 Journal Article %J Cr. Acad. Sci. I-Math, 2000, 330, 1013 %D 2000 %T Scalar curvature under boundary conditions %A Antonio Ambrosetti %A Li YanYan %A Andrea Malchiodi %B Cr. Acad. Sci. I-Math, 2000, 330, 1013 %I SISSA Library %G en %U http://hdl.handle.net/1963/1506 %1 2657 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:21Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1016/S0764-4442(00)00312-8 %0 Journal Article %J Differential Integral Equations 13 (2000) 1529-1550 %D 2000 %T The semigroup generated by a Temple class system with non-convex flux function %A Stefano Bianchini %X We consider the Cauchy problem for a nonlinear n × n system of conservation laws of Temple class, i.e. with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation. %B Differential Integral Equations 13 (2000) 1529-1550 %I Khayyam Publishing %G en_US %U http://hdl.handle.net/1963/3221 %1 1080 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-31T09:48:38Z\\nNo. of bitstreams: 1\\nsemigroup.pdf: 222652 bytes, checksum: 5d2014164bdd1a96e1c5213c5d4b61c9 (MD5) %0 Journal Article %J Discrete Contin. Dynam. Systems 6 (2000), no. 2, 329-350 %D 2000 %T On the shift differentiability of the flow generated by a hyperbolic system of conservation laws %A Stefano Bianchini %B Discrete Contin. Dynam. Systems 6 (2000), no. 2, 329-350 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/1274 %1 3181 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:38Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.3934/dcds.2000.6.329 %0 Journal Article %J Int. J. Mod. Phys. B 14 (2000) 2367-2382 %D 2000 %T Some Properties of Non-linear sigma-Models in Noncommutative Geometry %A Ludwik Dabrowski %A Thomas Krajewski %A Giovanni Landi %X We introduce non-linear $\\\\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some characteristic features of the corresponding $\\\\sigma$-models. In particular we construct a $\\\\sigma$-model instanton with topological charge equal to 1. We also define and investigate some properties of a noncommutative analogue of the Wess-Zumino-Witten model. %B Int. J. Mod. Phys. B 14 (2000) 2367-2382 %I SISSA Library %G en %U http://hdl.handle.net/1963/1373 %1 3082 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:57:00Z (GMT). No. of bitstreams: 1\\nhep-th0003099.pdf: 185777 bytes, checksum: 30806664c895808c1cb1afe5e6364f9f (MD5)\\n Previous issue date: 1999 %R 10.1142/S0217979200001898 %0 Journal Article %J Differential Integral Equations 13 (2000) 1503-1528 %D 2000 %T Stability of L^infty Solutions of Temple Class Systems %A Alberto Bressan %A Paola Goatin %XLet $u_t+f(u)_x=0$ be a strictly hyperbolic, genuinely nonlinear system of conservation laws of Temple class. In this paper, a continuous semigroup of solutions is constructed on a domain of $L^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the $L^1$ distance. Moreover, we show that a weak solution of the Cauchy problem coincides with the corresponding semigroup trajectory if and only if it satisfies an entropy condition of Oleinik type, concerning the decay of positive waves.

%B Differential Integral Equations 13 (2000) 1503-1528 %I Khayyam Publishing %G en_US %U http://hdl.handle.net/1963/3256 %1 1445 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-06T13:16:51Z\\nNo. of bitstreams: 1\\nTemple.pdf: 221742 bytes, checksum: a13773198af84c04068cf3021f12d3c8 (MD5) %0 Journal Article %D 2000 %T On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature %A Roberta Musina %A Paolo Caldiroli %I SISSA Library %G en %U http://hdl.handle.net/1963/1558 %1 2560 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:07Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Book Section %B Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109 %D 2000 %T Stokes Matrices for Frobenius Manifolds and the 6 Painlevé Equation %A Davide Guzzetti %K Painlevé equation %X These notes are a short review on the theory of Frobenius manifolds and its connection to problems of isomonodromy deformations and to Painlev'e equations. %B Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109 %I Kobe University, Japan %@ 4-907719-07-8 %G en %U http://hdl.handle.net/1963/6546 %1 6478 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T09:57:27Z No. of bitstreams: 1 03-RokkoLect00.pdf: 95063 bytes, checksum: 1b6fe9d8f1fe70ec5b8dec97d78fc55c (MD5) %0 Journal Article %J J. Geom. Phys. 35 (2000), no. 2-3, 239-272 %D 2000 %T Super KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy %A Gregorio Falqui %A Cesare Reina %A Alessandro Zampa %B J. Geom. Phys. 35 (2000), no. 2-3, 239-272 %I SISSA Library %G en %U http://hdl.handle.net/1963/1367 %1 3088 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:56:54Z (GMT). No. of bitstreams: 1\\nnlin.SI0001052.pdf: 330928 bytes, checksum: 88bf53e992f53f4e977dd5329347c85a (MD5)\\n Previous issue date: 1999 %R 10.1016/S0393-0440(00)00007-3 %0 Journal Article %D 1999 %T On the scalar curvature problem under symmetry %A Antonio Ambrosetti %A Andrea Malchiodi %I SISSA Library %G en %U http://hdl.handle.net/1963/1287 %1 3168 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:48Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116 %D 1999 %T Some properties of the solutions of obstacle problems with measure data %A Paolo Dall'Aglio %A Gianni Dal Maso %B Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116 %G en %U http://hdl.handle.net/1963/6432 %1 6372 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:18:45Z\\nNo. of bitstreams: 1\\nDAgl-DM-98.pdf: 205798 bytes, checksum: 96a8209dd814b3087f68a24a5f79d5b5 (MD5) %0 Journal Article %J Comm. Math. Phys. 207 (1999) 341-383 %D 1999 %T Stokes matrices and monodromy of the quantum cohomology of projective spaces %A Davide Guzzetti %X n this paper we compute Stokes matrices and monodromy of the quantum cohomology of projective spaces. This problem can be formulated in a \\\"classical\\\" framework, as the problem of computation of Stokes matrices and monodromy of differential equations with regular and irregular singularities. We prove that the Stokes\\\' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves. We also study the monodromy group of the quantum cohomology and we show that it is related to hyperbolic triangular groups. %B Comm. Math. Phys. 207 (1999) 341-383 %I Springer %G en_US %U http://hdl.handle.net/1963/3475 %1 789 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-29T17:01:09Z\\nNo. of bitstreams: 1\\n9904099v1.pdf: 477251 bytes, checksum: 6278f554f7fc5d2e100e89e3b236603a (MD5) %R 10.1007/s002200050729 %0 Journal Article %J Indiana Univ. Math. J. 48 (1999), no. 1, 43--84 %D 1999 %T Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws %A Alberto Bressan %A Philippe G. LeFloch %X The paper is concerned with the qualitative structure of entropy solutions to a strictly hyperbolic, genuinely nonlinear system of conservation laws. We first give an accurate description of the local and global wave-front structure of a BV solution, generated by a front tracking algorithm. %B Indiana Univ. Math. J. 48 (1999), no. 1, 43--84 %I Indiana University %G en_US %U http://hdl.handle.net/1963/3374 %1 956 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-01T09:02:14Z\\nNo. of bitstreams: 1\\nStructural_stability.pdf: 3175042 bytes, checksum: c04760cbf353315764f5aa8e879b0a62 (MD5) %R 10.1512/iumj.1999.48.1524 %0 Journal Article %J NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 %D 1998 %T Special functions with bounded variation and with weakly differentiable traces on the jump set %A Luigi Ambrosio %A Andrea Braides %A Adriana Garroni %B NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243 %I SISSA Library %G en %U http://hdl.handle.net/1963/1025 %1 2831 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:50Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Differential Integral Equations 10 (1997), no. 3, 401-418 %D 1997 %T The semigroup generated by a temple class system with large data %A Paolo Baiti %A Alberto Bressan %X We consider the Cauchy problem $$u_t + [F(u)]_x=0, u(0,x)=\\\\bar u(x) (*)$$ for a nonlinear $n\\\\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of (*) that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation. %B Differential Integral Equations 10 (1997), no. 3, 401-418 %I SISSA Library %G en %U http://hdl.handle.net/1963/1023 %1 2833 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:49Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. %D 1997 %T Shift-differentiability of the flow generated by a conservation law %A Alberto Bressan %A Graziano Guerra %X The paper introduces a notion of \\\"shift-differentials\\\" for maps with values in the space BV. These differentials describe first order variations of a given functin $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition. %B Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58. %I SISSA Library %G en %U http://hdl.handle.net/1963/1033 %1 2823 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:57Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Thesis %D 1997 %T Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains %A Rodica Toader %K Dirichlet problems %I SISSA %G en %U http://hdl.handle.net/1963/5698 %1 5541 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-04-12T11:43:37Z\\nNo. of bitstreams: 1\\nPhD_Toader_Rodica.pdf: 6894510 bytes, checksum: 8a7aced562b9372ebb9d7421262ea7f6 (MD5) %0 Journal Article %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396 %D 1997 %T Some properties of reachable solutions of nonlinear elliptic equations with measure data %A Gianni Dal Maso %A Annalisa Malusa %B Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396 %I SISSA %G en %U http://hdl.handle.net/1963/6434 %1 6375 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:33:05Z\\nNo. of bitstreams: 1\\nDM-Mal-97-sissa.pdf: 261079 bytes, checksum: bc786a00522c2b2dd3ee0acf0e9c3759 (MD5) %0 Journal Article %J Lett. Math. Phys. 40 (1997), no. 3, 235-256 %D 1997 %T Statistics in space dimension two %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Alessandro Teta %X We construct as a selfadjoint operator the Schroedinger hamiltonian for a system of $N$ identical particles on a plane, obeying the statistics defined by a representation $\\\\pi_1$ of the braid group. We use quadratic forms and potential theory, and give details only for the free case; standard arguments provide the extension of our approach to the case of potentials which are small in the sense of forms with respect to the laplacian. We also comment on the relation between the analysis given here and other approaches to the problem, and also on the connection with the description of a quantum particle on a plane under the influence of a shielded magnetic field (Aharanov-Bohm effect). %B Lett. Math. Phys. 40 (1997), no. 3, 235-256 %I SISSA Library %G en %U http://hdl.handle.net/1963/130 %1 12 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:22:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1996 %R 10.1023/A:1007361832622 %0 Journal Article %J Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 %D 1997 %T Structural stability for time-optimal planar sytheses %A Alberto Bressan %A Benedetto Piccoli %B Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371 %I SISSA Library %G en %U http://hdl.handle.net/1963/997 %1 2859 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:28Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Mat. Contemp. 10 (1996) 21-74 %D 1996 %T The semigroup approach to systems of conservation laws %A Alberto Bressan %B Mat. Contemp. 10 (1996) 21-74 %I Sociedade Brasileira de Matematica %G en %U http://hdl.handle.net/1963/1037 %1 2819 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:00Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Bull. Polish Acad. Sci. Math. 44 (1996), no. 4, 495--498 %D 1996 %T Solving Honig generic problem about Volterra integral equations %A Giovanni Vidossich %B Bull. Polish Acad. Sci. Math. 44 (1996), no. 4, 495--498 %I SISSA Library %G en %U http://hdl.handle.net/1963/941 %1 3513 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:40:46Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318 %D 1995 %T Some control problems for the pendulum %A Benedetto Piccoli %X The aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the difficulties one can encounter treating nonlinear systems. %B Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318 %I IEEE %G en %U http://hdl.handle.net/1963/982 %1 2874 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:16Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1109/CDC.1995.478998 %0 Journal Article %D 1995 %T Special functions of bounded deformation %A Giovanni Bellettini %A Alessandra Coscia %A Gianni Dal Maso %I SISSA Library %G en %U http://hdl.handle.net/1963/978 %1 3476 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Thesis %D 1992 %T Some Problems in the Calculus of the Variations %A Sandro Zagatti %K Calculus of variations %I SISSA %G en %U http://hdl.handle.net/1963/5428 %1 5260 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Stefania Cantagalli (cantagal@sissa.it) on 2012-02-10T13:58:54Z\\nNo. of bitstreams: 1\\nPhD_Zagatti_Sandro.pdf: 6337178 bytes, checksum: 121bfb32087688b7c579c8781e4cb5db (MD5) %0 Journal Article %J Appl.Math.Optim. 23 (1991), no.1, p. 17-49. %D 1991 %T Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions %A Giuseppe Buttazzo %A Gianni Dal Maso %B Appl.Math.Optim. 23 (1991), no.1, p. 17-49. %I SISSA Library %G en %U http://hdl.handle.net/1963/880 %1 2911 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:39:05Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Differential Integral Equations 4 (1991), no.4, p.739-765. %D 1991 %T On systems of ordinary differential equations with measures as controls %A Gianni Dal Maso %A Franco Rampazzo %B Differential Integral Equations 4 (1991), no.4, p.739-765. %I SISSA Library %G en %U http://hdl.handle.net/1963/840 %1 2951 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:35Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535. %D 1990 %T Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions %A Giuseppe Buttazzo %A Gianni Dal Maso %B Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535. %I SISSA Library %G en %U http://hdl.handle.net/1963/809 %1 2982 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:13Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Thesis %D 1989 %T Singular perturbation of the Laplacian and connections with models of random media %A Alessandro Teta %I SISSA %G en %U http://hdl.handle.net/1963/6348 %1 6281 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-12-20T10:24:13Z\\nNo. of bitstreams: 1\\nPhD_Teta_Alessandro.pdf: 7132993 bytes, checksum: 95123d37874902a4392f102bb70cd46f (MD5) %0 Journal Article %J Nonlinear Anal. 13 (1989), no. 10, 1171-1179 %D 1989 %T On the solvability of boundary value problems for higher order ordinary differential equations (Revised version) %A Giovanni Vidossich %B Nonlinear Anal. 13 (1989), no. 10, 1171-1179 %I SISSA Library %G en %U http://hdl.handle.net/1963/662 %1 3264 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:01Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %R 10.1016/0362-546X(89)90005-9 %0 Journal Article %J Nonlinear Anal. 13 (1989), no. 10, 1171-179 %D 1989 %T On the solvability of boundary value problems for higher order ordinary differential equations %A Giovanni Vidossich %B Nonlinear Anal. 13 (1989), no. 10, 1171-179 %I SISSA Library %G en %U http://hdl.handle.net/1963/631 %1 3822 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %R 10.1016/0362-546X(89)90005-9 %0 Journal Article %J Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990). %D 1989 %T Surfaces of minimal area enclosing a given body in R\\\\sp 3. %A Giovanni Mancini %A Roberta Musina %B Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990). %I SISSA Library %G en %U http://hdl.handle.net/1963/619 %1 3285 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:32Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J J.Funct.Anal. 79, 1988, no. 2, 476-492 %D 1988 %T Some properties of a class of nonlinear variational $m$-capacities %A Gianni Dal Maso %A Anneliese Defranceschi %B J.Funct.Anal. 79, 1988, no. 2, 476-492 %I SISSA Library %G en %U http://hdl.handle.net/1963/485 %1 3419 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:29Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %R 10.1016/0022-1236(88)90022-5 %0 Journal Article %D 1988 %T Susy-curves and supermoduli %A Gregorio Falqui %A Cesare Reina %I SISSA Library %G en %U http://hdl.handle.net/1963/761 %1 3030 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:37:15Z (GMT). No. of bitstreams: 1\\n169_88.pdf: 663959 bytes, checksum: 670b0ce089758e0cc68a21d0d2430c0c (MD5)\\n Previous issue date: 1988 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296 %D 1987 %T Solutions with minimal period for Hamiltonian systems in a potential well. %A Antonio Ambrosetti %A Vittorio Coti Zelati %B Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296 %I SISSA Library %G en %U http://hdl.handle.net/1963/466 %1 3437 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:32:46Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %0 Journal Article %J J. Differential Equations 67 (1987), no. 2, 165-184 %D 1987 %T Symmetry breaking in Hamiltonian systems %A Antonio Ambrosetti %A Vittorio Coti Zelati %A Ivar Ekeland %B J. Differential Equations 67 (1987), no. 2, 165-184 %I SISSA Library %G en %U http://hdl.handle.net/1963/409 %1 3558 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:32:09Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %0 Journal Article %J J. Funct. Anal. 62 (1985), no. 2, 119--159 %D 1985 %T Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets %A Gianni Dal Maso %B J. Funct. Anal. 62 (1985), no. 2, 119--159 %I SISSA Library %G en %U http://hdl.handle.net/1963/318 %1 3649 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:28:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1984 %0 Journal Article %J Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985 %D 1985 %T Some singular perturbation problems in the calculus of variations. %A Gianni Dal Maso %B Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985 %I SISSA Library %G en %U http://hdl.handle.net/1963/297 %1 3670 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:27:46Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1983 %0 Thesis %D 1984 %T Spin Structures and Global Conformal Transformations %A Ludwik Dabrowski %K Spinors %I SISSA %G en %U http://hdl.handle.net/1963/5854 %1 5718 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-18T10:02:53Z No. of bitstreams: 1 PhD_Dabrowski_Ludwik.pdf: 6031109 bytes, checksum: 45b102e8d5da1cb9575902b552e7b4e1 (MD5)