We 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.

}, author = {Marco Tezzele and Nicola Demo and Gianluigi Rozza} } @article {de2019sharp, title = {The sharp quantitative isocapacitary inequality}, year = {2019}, author = {Guido De Philippis and Michele Marini and Ekaterina Mukoseeva} } @article {2019, title = {On the square distance function from a manifold with boundary}, year = {2019}, abstract = {We 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.

}, url = {http://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf}, author = {Giovanni Bellettini and Alaa Elshorbagy} } @article {2019, title = {Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras}, journal = {arXiv e-prints}, year = {2019}, month = {May}, pages = {arXiv:1905.07730}, abstract = {We strengthen a result of Hanke{\textendash}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.

}, keywords = {Mathematics - K-Theory and Homology, Mathematics - Operator Algebras}, author = {Paolo Antonini and Buss, Alcides and Engel, Alexander and Siebenand , Timo} } @article {gigli2018second, title = {Second order differentiation formula on RCD(K, N) spaces}, journal = {Rendiconti Lincei-Matematica e Applicazioni}, volume = {29}, number = {2}, year = {2018}, pages = {377{\textendash}386}, author = {Nicola Gigli and Luca Tamanini} } @article {1802.02463, title = {Second order differentiation formula on RCD*(K,N) spaces}, year = {2018}, author = {Nicola Gigli and Luca Tamanini} } @conference {demo2018shape, title = {Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition}, booktitle = {Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship \& Maritime Research}, year = {2018}, publisher = {IOS Press}, organization = {IOS Press}, chapter = {212}, address = {Trieste, Italy}, abstract = {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.}, doi = {10.3233/978-1-61499-870-9-212}, url = {http://ebooks.iospress.nl/publication/49229}, author = {Nicola Demo and Marco Tezzele and Gianluca Gustin and Gianpiero Lavini and Gianluigi Rozza} } @article {riccobelli2017shape, title = {Shape transitions in a soft incompressible sphere with residual stresses}, journal = {Math. Mech. Solids}, volume = {23}, number = {12}, year = {2018}, pages = {1507{\textendash}1524}, publisher = {SAGE Publications Sage UK: London, England}, author = {Davide Riccobelli and Pasquale Ciarletta} } @article {doi:10.1080/14029251.2018.1503423, title = {Singular Hartree equation in fractional perturbed Sobolev spaces}, journal = {Journal of Nonlinear Mathematical Physics}, volume = {25}, number = {4}, year = {2018}, pages = {558-588}, publisher = {Taylor \& Francis}, abstract = {We 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 Schr{\"o}dinger 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.

}, doi = {10.1080/14029251.2018.1503423}, url = {https://doi.org/10.1080/14029251.2018.1503423}, author = {Alessandro Michelangeli and Alessandro Olgiati and Raffaele Scandone} } @article {1809.03586, title = {On some rigorous aspects of fragmented condensation}, year = {2018}, url = {https://arxiv.org/abs/1809.03586}, author = {Daniele Dimonte and Marco Falconi and Alessandro Olgiati} } @article {doi:10.1063/1.5026311, title = {Spectral triples on the Jiang-Su algebra}, journal = {Journal of Mathematical Physics}, volume = {59}, number = {5}, year = {2018}, pages = {053507}, doi = {10.1063/1.5026311}, url = {https://doi.org/10.1063/1.5026311}, author = {Jacopo Bassi and Ludwik Dabrowski} } @article {2018, title = {Stochastic homogenisation of free-discontinuity problems}, number = {SISSA;05/2018/MATE}, year = {2018}, abstract = {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.}, url = {http://preprints.sissa.it/handle/1963/35309}, author = {Filippo Cagnetti and Gianni Dal Maso and Lucia Scardia and Caterina Ida Zeppieri} } @article {doi:10.1098/rsta.2017.0424, title = {Symplectic invariants for parabolic orbits and cusp singularities of integrable systems}, journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {376}, number = {2131}, year = {2018}, pages = {20170424}, abstract = {We 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 {\textquoteleft}Finite dimensional integrable systems: new trends and methods{\textquoteright}.

}, doi = {10.1098/rsta.2017.0424}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0424}, author = {Alexey Bolsinov and Lorenzo Guglielmi and Elena Kudryavtseva} } @article {1701.03932, title = {Second order differentiation formula on compact RCD*(K,N) spaces}, year = {2017}, author = {Nicola Gigli and Luca Tamanini} } @article {2017, title = {Self-Adjoint Extensions of Dirac Operator with Coulomb Potential}, number = {SISSA;09/2017/MATE}, year = {2017}, institution = {SISSA}, abstract = {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) = {\O}(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.}, url = {http://urania.sissa.it/xmlui/handle/1963/35273}, author = {Matteo Gallone} } @article {2017, title = {Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei}, number = {SISSA;26/2017/MATE}, year = {2017}, abstract = {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 KreIn-Vi{\v s}ik- Birman extension scheme, or also on Grubb{\textquoteright}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.}, url = {http://preprints.sissa.it/handle/1963/35287}, author = {Matteo Gallone and Alessandro Michelangeli} } @article {2017, title = {Semistable Higgs Bundles on Calabi-Yau Manifolds}, number = {SISSA;40/2017/MATE;}, year = {2017}, abstract = {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.}, url = {http://preprints.sissa.it/handle/1963/35295}, author = {Ugo Bruzzo and Valeriano Lanza and Alessio Lo Giudice} } @article {Paoli2017, title = {Small Time Asymptotics on the Diagonal for H{\"o}rmander{\textquoteright}s Type Hypoelliptic Operators}, journal = {Journal of Dynamical and Control Systems}, volume = {23}, number = {1}, year = {2017}, month = {Jan}, pages = {111{\textendash}143}, abstract = {We compute the small time asymptotics of the fundamental solution of H{\"o}rmander{\textquoteright}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.

}, issn = {1573-8698}, doi = {10.1007/s10883-016-9321-z}, url = {https://doi.org/10.1007/s10883-016-9321-z}, author = {Elisa Paoli} } @article {ambrosi2017solid, title = {Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth}, journal = {J. Elast.}, volume = {129}, number = {1-2}, year = {2017}, pages = {107{\textendash}124}, publisher = {Springer Netherlands}, author = {D. Ambrosi and Pezzuto, S. and Davide Riccobelli and Stylianopoulos, T. and Pasquale Ciarletta} } @inbook {HessRozza2017, title = {A Spectral Element Reduced Basis Method in Parametric CFD}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017}, volume = {126}, year = {2017}, publisher = {Springer}, organization = {Springer}, chapter = {A Spectral Element Reduced Basis Method in Parametric CFD}, abstract = {We 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.

}, author = {Martin W. Hess and Gianluigi Rozza} } @conference {ENUMATH17_me, title = {A Spectral Element Reduced Basis Method in Parametric {CFD}}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017, Springer, in press}, year = {2017}, author = {Martin W. Hess and Gianluigi Rozza} } @article {2017, title = {Spectral Properties of the 2+1 Fermionic Trimer with Contact Interactions}, number = {SISSA;61/2017/MATE}, year = {2017}, note = {Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and Mathematical Physics" code RBFR13WAET (S.B., A.M., A.O.), by the DAAD International Trainership Programme (S.B.), and by a 2017 visiting research fellowship at the International Center for Mathematical Research CIRM, Trento (A.M.).}, publisher = {SISSA}, abstract = {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.}, url = {http://preprints.sissa.it/handle/1963/35303}, author = {Simon Becker and Alessandro Michelangeli and Andrea Ottolini} } @article {Gidoni2017, title = {Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler}, journal = {Meccanica}, volume = {52}, number = {3}, year = {2017}, month = {Feb}, pages = {587{\textendash}601}, abstract = {We 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.

}, issn = {1572-9648}, doi = {10.1007/s11012-016-0408-0}, url = {https://doi.org/10.1007/s11012-016-0408-0}, author = {Paolo Gidoni and Antonio DeSimone} } @article {Bertola:2015tg, title = {Symplectic geometry of the moduli space of projective structures in homological coordinates}, journal = {Inventiones Mathematicae}, year = {2017}, month = {06}, pages = {1{\textendash}56}, url = {https://arxiv.org/abs/1506.07918}, author = {Marco Bertola and Dmitry Korotkin and Chaya Norton} } @article {2016, title = {Second-order structured deformations}, year = {2016}, institution = {SISSA}, author = {Ana Cristina Barroso and Jose Matias and Marco Morandotti and David R. Owen} } @conference {mola2016ship, title = {Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model}, booktitle = {The 26th International Ocean and Polar Engineering Conference}, volume = {3}, year = {2016}, pages = {511{\textendash}518}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {BertoDiDub, title = {Simple Lie Algebras and Topological ODEs}, journal = {Int. Math. Res. Not.}, volume = {2016}, number = {rnw285}, year = {2016}, author = {Marco Bertola and Boris Dubrovin and Di Yang} } @article {BKT-sobolev, title = {On Sobolev instability of the interior problem of tomography}, journal = {Journal of Mathematical Analysis and Applications}, year = {2016}, author = {Marco Bertola and Alexander Katsevich and Alexander Tovbis} } @mastersthesis {2016, title = {Some results on quasistatic evolution problems for unidirectional processes}, year = {2016}, school = {SISSA}, author = {Vito Crismale} } @mastersthesis {2016, title = {Some results on the mathematical analysis of crack problems with forces applied on the fracture lips}, year = {2016}, school = {SISSA}, abstract = {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{\textquoteright}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.}, keywords = {Fracture mechanics}, author = {Stefano Almi} } @article {doi:10.1080/03605302.2015.1095766, title = {Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds}, journal = {Communications in Partial Differential Equations}, volume = {41}, number = {1}, year = {2016}, pages = {32-50}, publisher = {Taylor \& Francis}, abstract = {We 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{\textquoteright}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.

}, doi = {10.1080/03605302.2015.1095766}, url = {https://doi.org/10.1080/03605302.2015.1095766}, author = {Ugo Boscain and Dario Prandi and M. Seri} } @article {2016, title = {On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension}, year = {2016}, institution = {SISSA}, abstract = {We 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 $f{\textquoteright}{\textquoteright}=0$. 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.

}, url = {http://urania.sissa.it/xmlui/handle/1963/35209}, author = {Stefano Bianchini and Elio Marconi} } @article {Benvenuti2016, title = {Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {9}, year = {2016}, month = {Sep}, pages = {53}, abstract = {We 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.

}, issn = {1029-8479}, doi = {10.1007/JHEP09(2016)053}, url = {https://doi.org/10.1007/JHEP09(2016)053}, author = {Benvenuti, Sergio and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {farina2016symmetry, title = {Symmetry properties of some solutions to some semilinear elliptic equations}, journal = {Annali della Scuola Normale Superiore di Pisa. Classe di scienze}, volume = {16}, number = {4}, year = {2016}, pages = {1209{\textendash}1234}, publisher = {Classe di Scienze}, author = {Farina, Alberto and Andrea Malchiodi and Matteo Rizzi} } @article {2015, title = {Sch{\"o}dinger operators on half-line with shrinking potentials at the origin}, number = {SISSA;06/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We discuss the general model of a Schr{\"o}dinger 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.}, url = {http://urania.sissa.it/xmlui/handle/1963/34439}, author = {Gianfausto Dell{\textquoteright}Antonio and Alessandro Michelangeli} } @article {2015, title = {Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity}, year = {2015}, note = {The preprint is compsed of 37 pages and is recorded in PDF format}, abstract = {We 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.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34483}, author = {Lucia Tealdi and Giovanni Bellettini and Maurizio Paolini} } @mastersthesis {2015, title = {Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.}, year = {2015}, school = {SISSA}, abstract = {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.}, keywords = {Moser-Trudinger}, author = {Gabriele Mancini} } @article {2015, title = {Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results}, year = {2015}, abstract = {We 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.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34489}, author = {Gabriele Mancini} } @mastersthesis {2015, title = {Some results on anisotropic mean curvature and other phase-transition problems}, year = {2015}, school = {SISSA}, abstract = {The present thesis is divided into three parts. In the first part, we analyze a suitable regularization {\textemdash} which we call nonlinear multidomain model {\textemdash} 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{\textquoteright}s type problems based on the theory of coverings and of BV functions.}, keywords = {Anisotropic mean curvature}, author = {Stefano Amato} } @article {2015, title = {Stability of closed gaps for the alternating Kronig-Penney Hamiltonian}, number = {SISSA;16/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {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.}, url = {http://urania.sissa.it/xmlui/handle/1963/34460}, author = {Alessandro Michelangeli and Domenico Monaco} } @article {2015, title = {Stability of the (2+2)-fermionic system with zero-range interaction}, number = {SISSA;29/2015/MATE}, year = {2015}, note = {This SISSA preprint has 17 pages and recorded in PDF format}, abstract = {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.}, url = {http://urania.sissa.it/xmlui/handle/1963/34474}, author = {Alessandro Michelangeli and Paul Pfeiffer} } @article {2013, title = {Stable regular critical points of the Mumford-Shah functional are local minimizers}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {32}, number = {SISSA preprint;SISSA 33/2013/MATE}, year = {2015}, pages = {533-570}, publisher = {SISSA}, chapter = {533}, abstract = {In this paper it is shown that any regular critical point of the Mumford{\textendash}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.

}, doi = {10.1098/rspa.2015.0054}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @article {2015, title = {Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations}, number = {International Journal for Numerical Methods in Engineering;Volume 102, issue 5; pp.1136-1161;}, year = {2015}, publisher = {Wiley}, abstract = {In this work, we present a stable proper orthogonal decomposition{\textendash}Galerkin approximation for parametrized steady incompressible Navier{\textendash}Stokes equations with low Reynolds number.}, doi = {10.1002/nme.4772}, url = {http://urania.sissa.it/xmlui/handle/1963/34701}, author = {Francesco Ballarin and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2015, title = {Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry}, journal = {Acta Applicandae Mathematicae, vol. 137, Issue 1, 2015, pages: 185-203}, year = {2015}, note = {The article is composed of 23 pages and recorded in PDF format}, publisher = {Springer}, abstract = {We 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 r{\^o}le 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.

}, doi = {10.1007/s10440-014-9995-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34468}, author = {Domenico Monaco and Gianluca Panati} } @article {2014, title = {SBV Regularity of Systems of Conservation Laws and Hamilton{\textendash}Jacobi Equations}, number = {Journal of Mathematical Sciences;Volume 201; issue 6; pp. 733-745;}, year = {2014}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/s10958-014-2022-9}, url = {http://urania.sissa.it/xmlui/handle/1963/34691}, author = {Stefano Bianchini} } @article {2014, title = {Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional}, year = {2014}, note = {This article is composed if 33 pages and recorded in PDF format}, publisher = {SISSA}, abstract = {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.}, keywords = {Gamma-convergence, Cahn-Hilliard functional, phase transitions}, url = {http://hdl.handle.net/1963/7390}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2014, title = {Semiclassical limit of focusing NLS for a family of square barrier initial data}, number = {Communications on Pure and Applied Mathematics;volume 67; issue 2; pages 246-320;}, year = {2014}, publisher = {Wiley Periodicals}, abstract = {The small dispersion limit of the focusing nonlinear Schr{\"o}dinger 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.}, doi = {10.1002/cpa.21494}, url = {http://urania.sissa.it/xmlui/handle/1963/35066}, author = {Robert Jenkins and Kenneth McLaughlin} } @article {2014, title = {Shape control of active surfaces inspired by the movement of euglenids}, number = {Journal of the Mechanics and Physics of Solids;volume 62; issue 1; pages 99-112;}, year = {2014}, publisher = {Elsevier}, abstract = {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.}, doi = {10.1016/j.jmps.2013.09.017}, url = {http://urania.sissa.it/xmlui/handle/1963/35118}, author = {Marino Arroyo and Antonio DeSimone} } @article {2014, title = {Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows}, number = {Journal of scientific computing;volume 60; issue 3; pages 537-563;}, year = {2014}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/s10915-013-9807-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34698}, author = {Francesco Ballarin and Andrea Manzoni and Gianluigi Rozza and Sandro Salsa} } @article {berto-Tovbis-Katsevich-CPAM, title = {Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach}, journal = {Comm. Pure Appl. Math.}, year = {2014}, author = {Marco Bertola and Alexander Katsevich and Alexander Tovbis} } @article {2014, title = {Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics}, number = {Journal of high energy physics;volume 2014; issue 7; article number 141;}, year = {2014}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/JHEP07(2014)141}, url = {http://urania.sissa.it/xmlui/handle/1963/34546}, author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko} } @article {DANERI2014567, title = {Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {31}, number = {3}, year = {2014}, pages = {567 - 589}, abstract = {We 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.

}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2013.04.007}, url = {http://www.sciencedirect.com/science/article/pii/S0294144913000711}, author = {Sara Daneri and Aldo Pratelli} } @article {2014, title = {Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics}, number = {SISSA;53/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {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.}, url = {http://urania.sissa.it/xmlui/handle/1963/7463}, author = {Giuliano Lazzaroni and Riccarda Rossi and Marita Thomas and Rodica Toader} } @article {2014, title = {Some remarks on the seismic behaviour of embedded cantilevered retaining walls}, number = {Geotechnique;volume 64; issue 1; pages 40-50;}, year = {2014}, publisher = {Thomas Telford}, abstract = {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.}, doi = {10.1680/geot.13.P.031}, url = {http://urania.sissa.it/xmlui/handle/1963/35073}, author = {Riccardo Conti and F. Burali D{\textquoteright}Arezzo and Giulia M.B. Viggiani} } @article {2014, title = {Spontaneous division and motility in active nematic droplets}, number = {Physical review letters;volume 112; issue 14; article number 147802;}, year = {2014}, publisher = {American Physical Society}, abstract = {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.}, doi = {10.1103/PhysRevLett.112.147802}, url = {http://urania.sissa.it/xmlui/handle/1963/34902}, author = {Luca Giomi and Antonio DeSimone} } @article {2013, title = {Stability of equilibrium configurations for elastic films in two and three dimensions}, journal = {Advances in Calculus of Variations}, volume = {8}, number = {SISSA preprint;SISSA 38/2013/MATE}, year = {2014}, month = {01/2014}, pages = {117-153}, publisher = {SISSA}, chapter = {117}, abstract = {We 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.

}, keywords = {Epitaxially strained elastic films}, issn = {Online: 1864-8266; Print: 1864-8258}, doi = { https://doi.org/10.1515/acv-2013-0018}, url = {https://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml}, author = {Marco Bonacini} } @article {PacciariniRozza2014, title = {Stabilized reduced basis method for parametrized advection-diffusion PDEs}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {274}, year = {2014}, pages = {1{\textendash}18}, abstract = {In 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 {\textquoteleft}{\textquoteleft}double{\textquoteright}{\textquoteright} stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

}, doi = {10.1016/j.cma.2014.02.005}, author = {Pacciarini, P. and Gianluigi Rozza} } @conference {PacciariniRozza2014a, title = {Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher P{\'e}clet number: Roles of the boundary layers and inner fronts}, booktitle = {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}, year = {2014}, pages = {5614{\textendash}5624}, abstract = {Advection-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.

}, url = {https://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf}, author = {Pacciarini, P. and Gianluigi Rozza} } @article {2014, title = {Steady nearly incompressible vector elds in 2D: chain rule and renormalization}, year = {2014}, institution = {SISSA}, author = {Stefano Bianchini and N.A. Gusev} } @article {2014, title = {The stringy instanton partition function}, number = {Journal of high energy physics;volume 2014; issue 1; article number 038;}, year = {2014}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/JHEP01(2014)038}, url = {http://urania.sissa.it/xmlui/handle/1963/34589}, author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko} } @article {2014, title = {Structure of classical (finite and affine) W-algebras}, number = {arXiv:1404.0715;}, year = {2014}, note = {40 pages}, institution = {SISSA}, abstract = {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.}, url = {http://hdl.handle.net/1963/7314}, author = {Alberto De Sole and Victor G. Kac and Daniele Valeri} } @article {2014, title = {Structure of entropy solutions to general scalar conservation laws in one space dimension}, journal = {Journal of Mathematical Analysis and Applications}, volume = {428}, number = {SISSA;11/2014/MATE}, year = {2014}, month = {08/2015}, pages = {356-386}, publisher = {SISSA}, chapter = {356}, doi = {https://doi.org/10.1016/j.jmaa.2015.03.006}, url = {https://www.sciencedirect.com/science/article/pii/S0022247X15002218}, author = {Stefano Bianchini and Lei Yu} } @article {2014, title = {Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch}, number = {Journal of Applied Physics;volume 115; issue 8; article number 083505;}, year = {2014}, publisher = {American Institute of Physics}, abstract = {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.}, doi = {10.1063/1.4866576}, url = {http://urania.sissa.it/xmlui/handle/1963/35113}, author = {Alessandro Lucantonio and Paola Nardinocchi and Howard A. Stone} } @article {2014, title = {Swelling-induced and controlled curving in layered gel beams}, number = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;volume 470; issue 2171;}, year = {2014}, publisher = {Royal Society of London}, abstract = {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.}, doi = {10.1098/rspa.2014.0467}, url = {http://urania.sissa.it/xmlui/handle/1963/34987}, author = {Alessandro Lucantonio and Paola Nardinocchi and Matteo Pezzulla} } @article {1305.5271, title = {Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces}, year = {2013}, doi = {10.1016/j.jde.2015.10.011}, author = {Ugo Boscain and Dario Prandi} } @mastersthesis {2013, title = {Semistability and Decorated Bundles}, year = {2013}, school = {SISSA}, abstract = {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 {\textquotedblleft}enclose{\textquotedblright} 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.}, keywords = {Decorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf}, url = {http://hdl.handle.net/1963/7130}, author = {Andrea Pustetto} } @article {2013, title = {Softly Constrained Films}, number = {arXiv:1304.1077;}, year = {2013}, note = {Review article, 21 pages, 16 figures, submitted to Soft Matter}, publisher = {SISSA}, abstract = {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.}, url = {http://hdl.handle.net/1963/6563}, author = {Luca Giomi} } @mastersthesis {2013, title = {Some models of crack growth in brittle materials}, year = {2013}, school = {SISSA}, keywords = {Quasi-static crack evolution}, author = {Simone Racca} } @article {2013, title = {Some open problems}, number = {arXiv:1304.2590;}, year = {2013}, publisher = {SISSA}, abstract = {We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.}, keywords = {Geometry}, url = {http://hdl.handle.net/1963/7070}, author = {Andrei A. Agrachev} } @article {2001, title = {Some remarks on the viscous approximation of crack growth}, journal = {Discrete Contin. Dyn. Syst. Ser. S}, volume = {6}, number = {SISSA;24/2011/M}, year = {2013}, publisher = {SISSA}, chapter = {131-146}, abstract = {We 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.

}, keywords = {Variational models}, url = {http://hdl.handle.net/1963/4206}, author = {Giuliano Lazzaroni and Rodica Toader} } @mastersthesis {2013, title = {Some topics on Higgs bundles over projective varieties and their moduli spaces}, year = {2013}, school = {SISSA}, abstract = {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.}, keywords = {Algebraic Geometry, Moduli spaces, Vector bundles}, author = {Alessio Lo Giudice} } @article {MR3117621, title = {Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes}, journal = {J. Stat. Phys.}, volume = {153}, number = {4}, year = {2013}, pages = {654{\textendash}697}, issn = {0022-4715}, doi = {10.1007/s10955-013-0845-2}, url = {http://dx.doi.org/10.1007/s10955-013-0845-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {2013, title = {The splitting theorem in non-smooth context}, year = {2013}, abstract = {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 {\textquoteleft}infinitesimally Hilbertian{\textquoteright} 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.}, url = {http://preprints.sissa.it/handle/1963/35306}, author = {Nicola Gigli} } @article {2013, title = {Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control}, journal = {IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85}, year = {2013}, abstract = {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}, doi = {10.1109/TAC.2012.2206713}, url = {http://hdl.handle.net/1963/6503}, author = {Claudio Altafini and Francesco Ticozzi and K. Nishio} } @article {2012, title = {A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions}, journal = {Engineering Analysis with Boundary Elements, 37(1):128 {\textendash} 143, 2013.}, number = {SISSA;06/2012/M}, year = {2013}, publisher = {SISSA}, abstract = {We 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.

}, keywords = {Unsteady ship-wave interaction}, url = {http://hdl.handle.net/1963/5669}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {doi:10.1080/00036811.2011.628173, title = {Stable determination of a body immersed in a fluid: the nonlinear stationary case}, journal = {Applicable Analysis}, volume = {92}, number = {3}, year = {2013}, pages = {460-481}, publisher = {Taylor \& Francis}, abstract = {We 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{\textendash}Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log{\textendash}log type.

}, doi = {10.1080/00036811.2011.628173}, url = {https://doi.org/10.1080/00036811.2011.628173}, author = {Andrea Ballerini} } @article {ChenQuarteroniRozza2013, title = {Stochastic optimal robin boundary control problems of advection-dominated elliptic equations}, journal = {SIAM Journal on Numerical Analysis}, volume = {51}, number = {5}, year = {2013}, pages = {2700{\textendash}2722}, abstract = {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.}, doi = {10.1137/120884158}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {MR3088819, title = {Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model}, journal = {J. Math. Phys.}, volume = {54}, number = {4}, year = {2013}, pages = {043517, 25}, issn = {0022-2488}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @mastersthesis {2013, title = {The structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension}, year = {2013}, school = {SISSA}, abstract = {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: {\textbullet} SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. {\textbullet} Global structure of admissible BV solutions to strict hyperbolic conservation laws.}, author = {Lei Yu} } @article {1078-0947_2013_1_89, title = {Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {33}, number = {1078-0947_2013_1_8}, year = {2013}, pages = {89}, abstract = {We 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.

}, keywords = {lower and upper solutions, parameter dependent equations, Periodic solutions, Poincar{\'e}-Birkhoff twist theorem, subharmonic solutions}, issn = {1078-0947}, doi = {10.3934/dcds.2013.33.89}, url = {http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {2013, title = {On Sudakov{\textquoteright}s type decomposition of transference plans with norm costs}, number = {SISSA;51/2013/MATE}, year = {2013}, institution = {SISSA}, url = {http://hdl.handle.net/1963/7206}, author = {Stefano Bianchini and Sara Daneri} } @article {2013, title = {Symplectic instanton bundles on P3 and {\textquoteright}t Hooft instantons}, year = {2013}, note = {This preprint has been published with the title "Moduli of symplectic instanton vector bundles of higher rank on projective space P-3 " in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, Volume: 10, issue 4, Augst 2012, pages 1232-1245.}, institution = {arXiv:1312.5554 [math.AG]}, abstract = {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 {\textquoteright}t Hooft instantons.}, url = {http://urania.sissa.it/xmlui/handle/1963/34486}, author = {Ugo Bruzzo and Dimitri Markushevich and Alexander Tikhomirov} } @article {2012, title = {SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension}, journal = {Communications in Mathematical Physics 313 (2012) 1-33}, number = {SISSA;71/2010/M}, year = {2012}, publisher = {Springer}, doi = {10.1007/s00220-012-1480-5}, url = {http://hdl.handle.net/1963/4091}, author = {Stefano Bianchini and Laura Caravenna} } @article {2011, title = {SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)}, journal = {Siam Journal on Mathematical Analysis}, volume = {44}, number = {SISSA;13/2011/M}, year = {2012}, pages = {2179-2203}, publisher = {SISSA}, doi = {10.1137/110827272}, url = {http://hdl.handle.net/20.500.11767/14066}, author = {Stefano Bianchini and Daniela Tonon} } @article {2012, title = {SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension}, journal = {Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388}, year = {2012}, publisher = {Elsevier}, abstract = {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}, keywords = {Hyperbolic systems}, doi = {10.1016/S0252-9602(12)60024-1}, url = {http://hdl.handle.net/1963/6535}, author = {Stefano Bianchini} } @article {bianchini2012sbv, title = {SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension}, journal = {Rend. Istit. Mat. Univ. Trieste}, volume = {44}, year = {2012}, pages = {439{\textendash}472}, author = {Stefano Bianchini and Lei Yu} } @article {2012, title = {SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian}, journal = {Journal of Mathematical Analysis and Applications}, volume = {391}, number = {SISSA;45/2011/M}, year = {2012}, pages = {190-208}, publisher = {SISSA}, doi = {10.1016/j.jmaa.2012.02.017}, url = {http://hdl.handle.net/20.500.11767/13909}, author = {Stefano Bianchini and Daniela Tonon} } @article {1078-0947_2012_4_1125, title = {Second order approximations of quasistatic evolution problems in finite dimension}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {32}, number = {1078-0947_2012_4_112}, year = {2012}, pages = {1125}, abstract = {In 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.

}, keywords = {discrete approximations, perturbation methods, saddle-node bifurcation, Singular perturbations, vanishing viscosity}, issn = {1078-0947}, doi = {10.3934/dcds.2012.32.1125}, url = {http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8}, author = {Virginia Agostiniani} } @article {doi:10.1080/17513758.2011.611260, title = {Self-propelled micro-swimmers in a Brinkman fluid}, journal = {Journal of Biological Dynamics}, volume = {6}, number = {sup1}, year = {2012}, note = {PMID: 22873677}, pages = {88-103}, publisher = {Taylor \& Francis}, abstract = {We 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.

}, doi = {10.1080/17513758.2011.611260}, url = {https://doi.org/10.1080/17513758.2011.611260}, author = {Marco Morandotti} } @article {10671, title = {Simulation-based uncertainty quantification of human arterial network hemodynamics}, journal = {International Journal Numerical Methods Biomedical Engineering}, number = {SISSA preprint;}, year = {2012}, publisher = {Wiley}, abstract = {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.}, keywords = {uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction}, author = {Peng Chen and Alfio Quarteroni and Gianluigi Rozza} } @article {Berti20122579, title = {Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential}, journal = {Nonlinearity}, volume = {25}, number = {9}, year = {2012}, note = {cited By (since 1996)3}, pages = {2579-2613}, abstract = {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 {\textquoteright}separation properties{\textquoteright} of the small divisors assuming weaker non-resonance conditions than in [11]. {\textcopyright} 2012 IOP Publishing Ltd.}, issn = {09517715}, doi = {10.1088/0951-7715/25/9/2579}, author = {Massimiliano Berti and Philippe Bolle} } @article {2012, title = {Solving the Sixth Painlev{\'e} Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae}, journal = {Int Math Res Notices (2012) 2012 (6): 1352-1413}, number = {arXiv:1010.1895;}, year = {2012}, note = {53 pages, 2 figures}, publisher = {Oxford University Press}, abstract = {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.}, doi = {10.1093/imrn/rnr071}, url = {http://hdl.handle.net/1963/6093}, author = {Davide Guzzetti} } @article {tonon2012some, title = {Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles}, journal = {Riv. Mat. Univ. Parma}, volume = {3}, number = {1}, year = {2012}, pages = {163{\textendash}175}, abstract = {We 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.

}, url = {https://hal.archives-ouvertes.fr/hal-00918409}, author = {Daniela Tonon} } @mastersthesis {2012, title = {Some aspects of spinors {\textendash} classical and noncommutative}, year = {2012}, school = {SISSA}, url = {http://hdl.handle.net/1963/6317}, author = {Giacomo Dossena} } @article {2012, title = {Some remarks on quantum mechanics}, journal = {International Journal of Geometric Methods in Modern Physics, Volume 9, Issue 2, March 2012, Article number1260018}, year = {2012}, publisher = {World Scientific Publishing}, abstract = {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.}, keywords = {Quantum mechanics}, doi = {10.1142/S0219887812600183}, url = {http://hdl.handle.net/1963/7018}, author = {Gianfausto Dell{\textquoteright}Antonio} } @article {MR2880030, title = {Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes}, journal = {J. Stat. Phys.}, volume = {146}, number = {3}, year = {2012}, pages = {475{\textendash}518}, issn = {0022-4715}, doi = {10.1007/s10955-011-0409-2}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {2012, title = {Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions}, journal = {Rev. Math. Phys. 24 (2012), 1250017}, number = {arXiv:1201.5740;}, year = {2012}, publisher = {World Scientific}, abstract = {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.}, doi = {10.1142/S0129055X12500171}, url = {http://hdl.handle.net/1963/6069}, author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Domenico Finco and Alessandro Michelangeli and Alessandro Teta} } @conference {Mola2012, title = {A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves}, booktitle = {17th Int. Conf. Ships Shipp. Res.}, year = {2012}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {2012, title = {Sub-Riemannian structures on 3D Lie groups}, journal = {Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44}, number = {arXiv:1007.4970;}, year = {2012}, publisher = {SISSA}, abstract = {We 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.

}, doi = {10.1007/s10883-012-9133-8}, url = {http://hdl.handle.net/1963/6453}, author = {Andrei A. Agrachev and Davide Barilari} } @article {2012, title = {Systems of Quadratic Inequalities}, journal = {Proceedings of the London Mathematical Society, Volume 105, Issue 3, September 2012, Pages 622-660}, number = {arXiv:1012.5731;}, year = {2012}, publisher = {SISSA}, abstract = {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.}, doi = {DOI: 10.1112/plms/pds010}, url = {http://hdl.handle.net/1963/7072}, author = {Andrei A. Agrachev and Antonio Lerario} } @article {2011, title = {SBV regularity for Hamilton-Jacobi equations in R^n}, journal = {Arch. Rational Mech. Anal. 200 (2011) 1003-1021}, number = {arXiv:1002.4087;}, year = {2011}, publisher = {Springer}, abstract = {In 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 $SBV_{loc}(\Omega)$.

}, doi = {10.1007/s00205-010-0381-z}, url = {http://hdl.handle.net/1963/4911}, author = {Stefano Bianchini and Camillo De Lellis and Roger Robyr} } @article {2011, title = {Semistable and numerically effective principal (Higgs) bundles}, journal = {Advances in Mathematics 226 (2011) 3655-3676}, number = {SISSA;27/2009/FM}, year = {2011}, publisher = {Elsevier}, abstract = {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{\textendash}Yang{\textendash}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.}, doi = {10.1016/j.aim.2010.10.026}, url = {http://hdl.handle.net/1963/3638}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2011, title = {Singular perturbation models in phase transitions for second order materials}, journal = {Indiana Univ. Math. J. 60 (2011) 367-409}, number = {SISSA;20/2010/M}, year = {2011}, publisher = {Indiana University}, abstract = {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.}, doi = {10.1512/iumj.2011.60.4346}, url = {http://hdl.handle.net/1963/3858}, author = {Milena Chermisi and Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @inbook {2011, title = {Solving PVI by Isomonodromy Deformations}, booktitle = {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}, number = {arXiv:1106.2636;}, year = {2011}, note = {12 pages, 1 figurethis paper has been}, publisher = {SISSA}, organization = {SISSA}, abstract = {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.}, keywords = {Painlevé Equations}, isbn = {9783110275582}, url = {http://hdl.handle.net/1963/6522}, author = {Davide Guzzetti} } @article {2011, title = {On the Space of Symmetric Operators with Multiple Ground States}, journal = {Functional Analysis and its Applications, Volume 45, Issue 4, December 2011, Pages 241-251}, number = {arXiv:1107.3010;}, year = {2011}, publisher = {SISSA}, abstract = {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.}, keywords = {Multiple eigenvalue}, doi = {DOI: 10.1007/s10688-011-0026-5}, url = {http://hdl.handle.net/1963/7069}, author = {Andrei A. Agrachev} } @article {2011, title = {The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry}, journal = {Journal of Dynamical and Control Systems }, volume = {17 }, number = {arXiv:1009.2612;}, year = {2011}, pages = {141-161}, publisher = {Springer}, abstract = {We 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.

}, doi = {10.1007/s10883-011-9113-4}, url = {http://hdl.handle.net/1963/4914}, author = {Bernard Bonnard and Gr{\'e}goire Charlot and Roberta Ghezzi and Gabriel Janin} } @article {2011, title = {Structure of level sets and Sard-type properties of Lipschitz maps}, number = {SISSA;51/2011/M}, year = {2011}, institution = {SISSA}, url = {http://hdl.handle.net/1963/4657}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {boscaggin2011subharmonic, title = {Subharmonic solutions of planar Hamiltonian systems: a rotation number approach}, journal = {Advanced Nonlinear Studies}, volume = {11}, number = {1}, year = {2011}, pages = {77{\textendash}103}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2011-0104}, author = {Alberto Boscaggin} } @article {boscaggin2011subharmonic, title = {Subharmonic solutions of planar Hamiltonian systems via the Poincar{\'e}́-Birkhoff theorem}, journal = {Le Matematiche}, volume = {66}, number = {1}, year = {2011}, pages = {115{\textendash}122}, abstract = {We 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.

}, author = {Alberto Boscaggin} } @article {2011, title = {Supercritical conformal metrics on surfaces with conical singularities}, journal = {Int Math Res Notices (2011) 2011 (24): 5625-5643}, number = {SISSA;56/2010/M}, year = {2011}, publisher = {Oxford University Press}, abstract = {We 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.

}, doi = {10.1093/imrn/rnq285}, url = {http://hdl.handle.net/1963/4095}, author = {Mauro Bardelloni and Francesca De Marchis and Andrea Malchiodi} } @article {2011, title = {A system-level approach for deciphering the transcriptional response to prion infection}, journal = {Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14}, number = {PMID:22016408;}, year = {2011}, publisher = {Oxford University Press}, abstract = {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.}, doi = {10.1093/bioinformatics/btr580}, url = {http://hdl.handle.net/1963/5745}, author = {Mattia Zampieri and Giuseppe Legname and Daniel Segr{\`e} and Claudio Altafini} } @article {selvitella2010, title = {Semiclassical evolution of two rotating solitons for the Nonlinear Schr{\"o}dinger Equation with electric potential}, journal = {Adv. Differential Equations}, volume = {15}, number = {3/4}, year = {2010}, month = {03}, pages = {315{\textendash}348}, publisher = {Khayyam Publishing, Inc.}, url = {https://projecteuclid.org:443/euclid.ade/1355854752}, author = {Alessandro Selvitella} } @article {2010, title = {On semistable principal bundles over complex projective manifolds, II}, journal = {Geom. Dedicata 146 (2010) 27-41}, number = {SISSA;85/2008/FM}, year = {2010}, abstract = {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.}, doi = {10.1007/s10711-009-9424-8}, url = {http://hdl.handle.net/1963/3404}, author = {Indranil Biswas and Ugo Bruzzo} } @article {2010, title = {Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials}, number = {SISSA;31/2010/M}, year = {2010}, abstract = {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.}, url = {http://hdl.handle.net/1963/3869}, author = {Mouhamed Moustapha Fall and Roberta Musina} } @article {2010, title = {Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295}, number = {SISSA;12/2008/M}, year = {2010}, abstract = {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.}, doi = {10.2422/2036-2145.2010.2.02}, url = {http://hdl.handle.net/1963/2601}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {Berti2009609, title = {Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions}, journal = {Archive for Rational Mechanics and Analysis}, volume = {195}, number = {2}, year = {2010}, note = {cited By (since 1996)6}, pages = {609-642}, abstract = {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". {\textcopyright} Springer-Verlag (2009).}, issn = {00039527}, doi = {10.1007/s00205-008-0211-8}, author = {Massimiliano Berti and Philippe Bolle} } @article {2010, title = {Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit}, journal = {SIAM J. Math. Anal. 42 (2010) 2132-2154}, number = {SISSA;09/2010/FM}, year = {2010}, abstract = {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.}, doi = {10.1137/090779103}, url = {http://hdl.handle.net/1963/3839}, author = {Tamara Grava and Tom Claeys} } @article {Ballerini_2010, title = {Stable determination of an immersed body in a stationary Stokes fluid}, journal = {Inverse Problems}, volume = {26}, number = {12}, year = {2010}, month = {nov}, pages = {125015}, publisher = {IOP Publishing}, abstract = {We 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{\textendash}log type.

}, doi = {10.1088/0266-5611/26/12/125015}, url = {https://doi.org/10.1088\%2F0266-5611\%2F26\%2F12\%2F125015}, author = {Andrea Ballerini} } @article {2009, title = {On a Sobolev type inequality related to the weighted p-Laplace operator}, journal = {J. Math. Anal. Appl. 352 (2009) 99-111}, number = {SISSA;18/2008/M}, year = {2009}, doi = {10.1016/j.jmaa.2008.06.021}, url = {http://hdl.handle.net/1963/2613}, author = {Marita Gazzini and Roberta Musina} } @article {doi:10.1142/S0218202509003589, title = {Solutions of the Schr{\"o}dinger{\textendash}Poisson problem concentrating on spheres, part I: necessary conditions}, journal = {Mathematical Models and Methods in Applied Sciences}, volume = {19}, number = {05}, year = {2009}, pages = {707-720}, abstract = {In this paper we study a coupled nonlinear Schr{\"o}dinger{\textendash}Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schr{\"o}dinger 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.

}, doi = {10.1142/S0218202509003589}, url = {https://doi.org/10.1142/S0218202509003589}, author = {Ianni, Isabella and Giusi Vaira} } @article {2009, title = {Some new entire solutions of semilinear elliptic equations on Rn}, journal = {Adv. Math. 221 (2009) 1843-1909}, year = {2009}, publisher = {Elsevier}, doi = {10.1016/j.aim.2009.03.012}, url = {http://hdl.handle.net/1963/3645}, author = {Andrea Malchiodi} } @article {2009, title = {Strain-order coupling in nematic elastomers: equilibrium configurations}, journal = {Math. Models Methods Appl. Sci. 19 (2009) 601-630}, number = {SISSA;24/2008/M}, year = {2009}, abstract = {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.}, url = {http://hdl.handle.net/1963/2700}, author = {Pierluigi Cesana and Antonio DeSimone} } @article {2009, title = {Stratos: a code for 3D free surface flows with floating constraints}, number = {SISSA;41/2009/M}, year = {2009}, abstract = {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......}, url = {http://hdl.handle.net/1963/3701}, author = {Antonio DeSimone and B. Bianchi and Luca Heltai} } @article {2008, title = {A second order minimality condition for the Mumford-Shah functional}, journal = {Calc. Var. Partial Differential Equations 33 (2008) 37-74}, number = {SISSA;82/2006/M}, year = {2008}, abstract = {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.}, doi = {10.1007/s00526-007-0152-3}, url = {http://hdl.handle.net/1963/1955}, author = {Filippo Cagnetti and Maria Giovanna Mora and Massimiliano Morini} } @article {2008, title = {On semistable principal bundles over a complex projective manifold}, journal = {Int. Math. Res. Not. vol. 2008, article ID rnn035}, number = {arXiv.org;0803.4042v1}, year = {2008}, publisher = {Oxford University Press}, abstract = {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.}, doi = {10.1093/imrn/rnn035}, url = {http://hdl.handle.net/1963/3418}, author = {Indranil Biswas and Ugo Bruzzo} } @article {2008, title = {Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn}, journal = {J. Funct. Anal. 254 (2008) 2816-2845}, number = {SISSA;73/2007/M}, year = {2008}, abstract = {Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schr{\"o}dinger equations.}, doi = {10.1016/j.jfa.2007.11.013}, url = {http://hdl.handle.net/1963/2175}, author = {Antonio Ambrosetti and Giovanna Cerami and David Ruiz} } @article {2008, title = {Stability of planar switched systems: the nondiagonalizable case}, journal = {Commun. Pure Appl. Anal. 7 (2008) 1-21}, number = {SISSA;44/2006/M}, year = {2008}, doi = {10.3934/cpaa.2008.7.1}, url = {http://hdl.handle.net/1963/1857}, author = {Ugo Boscain and Moussa Balde} } @article {2008, title = {Symmetric obstruction theories and Hilbert schemes of points on threefolds}, journal = {Algebra Number Theory 2 (2008) 313-345}, number = {arXiv.org;math/0512556v1}, year = {2008}, abstract = {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.}, url = {http://hdl.handle.net/1963/2709}, author = {Kai Behrend and Barbara Fantechi} } @mastersthesis {2008, title = {Symmetries of noncommutative spaces and equivariant cohomology}, year = {2008}, school = {SISSA}, abstract = {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{\textasciimacron}ne algebraic models for the equivariant cohomology of such actions.}, keywords = {Noncommutative spaces}, url = {http://hdl.handle.net/1963/5254}, author = {Lucio Cirio} } @article {2007, title = {Semistable principal Higgs bundles}, number = {SISSA;89/2007/MP}, year = {2007}, url = {http://hdl.handle.net/1963/2533}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2007, title = {Smooth toric DM stacks}, number = {SISSA;64/2007/MP}, year = {2007}, abstract = {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.}, url = {http://hdl.handle.net/1963/2120}, author = {Barbara Fantechi and Etienne Mann and Fabio Nironi} } @article {2007, title = {Soft elasticity and microstructure in smectic C elastomers}, number = {SISSA;05/2006/M}, year = {2007}, abstract = {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.}, doi = {10.1007/s00161-006-0031-8}, url = {http://hdl.handle.net/1963/1811}, author = {Antonio DeSimone and James Adams and Sergio Conti} } @article {2007, title = {Solutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals}, journal = {J. Math. Anal. Appl. 335 (2007) 1143-1160}, year = {2007}, abstract = {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.}, doi = {10.1016/j.jmaa.2007.02.034}, url = {http://hdl.handle.net/1963/2763}, author = {Sandro Zagatti} } @article {2007, title = {Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result}, number = {SISSA;52/2007/M}, year = {2007}, abstract = {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.}, url = {http://hdl.handle.net/1963/2111}, author = {Fethi Mahmoudi and Andrea Malchiodi} } @article {2007, title = {Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions}, number = {SISSA;51/2007/M}, year = {2007}, abstract = {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.}, url = {http://hdl.handle.net/1963/2112}, author = {Fethi Mahmoudi and Andrea Malchiodi and Marcelo Montenegro} } @article {2007, title = {Some existence results for the Toda system on closed surfaces}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412}, number = {SISSA;75/2005/M}, year = {2007}, abstract = {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 $\\\\rho_2 < 4 \\\\pi$.}, doi = {10.4171/RLM/504}, url = {http://hdl.handle.net/1963/1775}, author = {Andrea Malchiodi and Cheikh Birahim Ndiaye} } @article {2007, title = {Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws}, journal = {NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592}, number = {SISSA;68/2005/M}, year = {2007}, doi = {10.1007/s00030-007-5010-7}, url = {http://hdl.handle.net/1963/1769}, author = {Andrea Marson and Carlotta Donadello} } @article {2007, title = {Standing waves of some coupled Nonlinear Schr{\"o}dinger Equations}, number = {SISSA;02/2006/M}, year = {2007}, abstract = {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.}, doi = {10.1112/jlms/jdl020}, url = {http://hdl.handle.net/1963/1821}, author = {Antonio Ambrosetti and Eduardo Colorado} } @article {2007, title = {Strengthened convergence of marginals to the cubic nonlinear Schroedinger equation}, number = {SISSA;35/2007/MP}, year = {2007}, abstract = {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.}, url = {http://hdl.handle.net/1963/1977}, author = {Alessandro Michelangeli} } @article {2007, title = {Surfactants in Foam Stability: A Phase-Field Model}, journal = {Arch. Rational Mech. Anal. 183 (2007) 411-456}, year = {2007}, abstract = {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.}, doi = {10.1007/s00205-006-0012-x}, url = {http://hdl.handle.net/1963/2035}, author = {Irene Fonseca and Massimiliano Morini and Valeriy Slastikov} } @article {Bertola:Semiiso, title = {Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions}, journal = {Comm. Math. Phys.}, volume = {263}, number = {2}, year = {2006}, pages = {401{\textendash}437}, issn = {0010-3616}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {2006, title = {Semistability vs. nefness for (Higgs) vector bundles}, journal = {Differential Geom. Appl. 24 (2006) 403-416}, number = {arXiv.org;math/0310040v3}, year = {2006}, abstract = {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.}, doi = {10.1016/j.difgeo.2005.12.007}, url = {http://hdl.handle.net/1963/2237}, author = {Ugo Bruzzo and Daniel Hernandez Ruiperez} } @article {2006, title = {On Separation of Variables for Homogeneous SL(r) Gaudin Systems}, number = {SISSA;106/2003/FM}, year = {2006}, abstract = {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.}, doi = {10.1007/s11040-006-9012-1}, url = {http://hdl.handle.net/1963/2538}, author = {Gregorio Falqui and Fabio Musso} } @article {2006, title = {Spectral geometry of k-Minkowski space}, journal = {J. Math. Phys. 47 (2006) 062105}, number = {arXiv.org;hep-th/0503012v4}, year = {2006}, abstract = {After recalling Snyder{\textquoteright}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{\textquoteright}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.

}, doi = {10.1063/1.2204808}, url = {http://hdl.handle.net/1963/2131}, author = {Francesco D{\textquoteright}Andrea} } @article {2006, title = {Stability of planar nonlinear switched systems}, number = {SISSA;04/2005/M}, year = {2006}, abstract = {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,$\infty$) {\textrightarrow} {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.}, url = {http://hdl.handle.net/1963/1710}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Mario Sigalotti} } @article {2005, title = {Self-similar folding patterns and energy scaling in compressed elastic sheets}, journal = {Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549}, year = {2005}, publisher = {Elsevier}, abstract = {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.}, doi = {10.1016/j.cma.2004.07.044}, url = {http://hdl.handle.net/1963/3000}, author = {Sergio Conti and Antonio DeSimone and Stefan M{\"u}ller} } @inbook {2005, title = {A short introduction to optimal control}, booktitle = {Contr{\^o}le non lin{\'e}aire et applications: Cours donn{\'e}s {\`a} l\\\'{\'e}cole d\\\'{\'e}t{\'e} du Cimpa de l\\\'Universit{\'e} de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005}, number = {SISSA;10/2004/M}, year = {2005}, isbn = {2 7056 6511 0}, url = {http://hdl.handle.net/1963/2257}, author = {Ugo Boscain and Benedetto Piccoli} } @booklet {2005, title = {Solutions of Neumann problems in domains with cracks and applications to fracture mechanics}, number = {arXiv.org;math.AP/0105132}, year = {2005}, url = {http://hdl.handle.net/1963/1684}, author = {Gianni Dal Maso} } @article {2005, title = {The spectral geometry of the equatorial Podles sphere}, journal = {C. R. Math. 340 (2005) 819-822}, number = {SISSA;71/2004/FM}, year = {2005}, abstract = {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.}, doi = {10.1016/j.crma.2005.04.003}, url = {http://hdl.handle.net/1963/2275}, author = {Ludwik Dabrowski and Giovanni Landi and Mario Paschke and Andrzej Sitarz} } @article {2005, title = {Stability of solutions of quasilinear parabolic equations}, journal = {J. Math. Anal. Appl. 308 (2005) 221-239}, number = {SISSA;51/2003/M}, year = {2005}, publisher = {Elsevier}, abstract = {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.}, doi = {10.1016/j.jmaa.2005.01.026}, url = {http://hdl.handle.net/1963/2892}, author = {Giuseppe Maria Coclite and Helge Holden} } @article {2005, title = {Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains}, journal = {Int. J. Numer. Anal. Met. 29 (2005) 73-101}, number = {SISSA;74/2004/M}, year = {2005}, abstract = {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.}, doi = {10.1002/nag.405}, url = {http://hdl.handle.net/1963/2165}, author = {Antonio DeSimone and Claudio Tamagnini} } @article {2004, title = {Semiclassical analysis of constrained quantum systems}, journal = {J. Phys. A 37 (2004) 5605-5624}, number = {arXiv.org;math-ph/0312034v2}, year = {2004}, publisher = {IOP Publishing}, abstract = {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.}, doi = {10.1088/0305-4470/37/21/007}, url = {http://hdl.handle.net/1963/2997}, author = {Gianfausto Dell{\textquoteright}Antonio and Lucattilio Tenuta} } @article {2004, title = {Semi-cooperative strategies for differential games}, journal = {Internat. J. Game Theory 32 (2004) 561-593}, number = {SISSA;103/2003/M}, year = {2004}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/s001820400180}, url = {http://hdl.handle.net/1963/2893}, author = {Alberto Bressan and Wen Shen} } @article {2004, title = {A sharp decay estimate for positive nonlinear waves}, journal = {SIAM J. Math. Anal. 36 (2004) 659-677}, number = {SISSA;59/2003/M}, year = {2004}, publisher = {SIAM}, abstract = {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.}, doi = {10.1137/S0036141003427774}, url = {http://hdl.handle.net/1963/2916}, author = {Alberto Bressan and Tong Yang} } @article {2004, title = {Singular Z_N curves, Riemann-Hilbert problem and modular solutions of the Schlesinger equation}, journal = {Int. Math. Res. Not. 2004, no. 32, 1619-1683}, number = {arXiv.org;math-ph/0306050}, year = {2004}, abstract = {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.}, doi = {10.1155/S1073792804132625}, url = {http://hdl.handle.net/1963/2540}, author = {Victor Z. Enolski and Tamara Grava} } @article {2004, title = {Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II}, journal = {Indiana Univ. Math. J. 53 (2004) 297-392}, number = {SISSA;93/2002/M}, year = {2004}, publisher = {Indiana University Mathematics Journal}, doi = {10.1512/iumj.2004.53.2400}, url = {http://hdl.handle.net/1963/1663}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @article {2004, title = {Small BV solutions of hyperbolic noncooperative differential games}, journal = {SIAM J. Control Optim. 43 (2004) 194-215}, number = {SISSA;21/2003/M}, year = {2004}, publisher = {SIAM}, abstract = {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.}, doi = {10.1137/S0363012903425581}, url = {http://hdl.handle.net/1963/2917}, author = {Alberto Bressan and Wen Shen} } @article {2004, title = {Solitary waves for Maxwell Schrodinger equations}, journal = {Electron. J. Differential Equations (2004) 94}, number = {SISSA;11/2002/M}, year = {2004}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/1582}, author = {Giuseppe Maria Coclite and Vladimir Georgiev} } @article {2004, title = {Solutions concentrating at curves for some singularly perturbed elliptic problems}, journal = {C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780}, year = {2004}, publisher = {Elsevier}, doi = {10.1016/j.crma.2004.03.023}, url = {http://hdl.handle.net/1963/4869}, author = {Andrea Malchiodi} } @article {2004, title = {Soluzioni periodiche di PDEs Hamiltoniane}, journal = {Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661}, year = {2004}, publisher = {Unione Matematica Italiana}, url = {http://hdl.handle.net/1963/4582}, author = {Massimiliano Berti} } @article {2004, title = {Some remarks on multidimensional systems of conservation laws}, journal = {Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233}, year = {2004}, publisher = {Accademia Nazionale dei Lincei}, abstract = {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.}, url = {http://hdl.handle.net/1963/3642}, author = {Alberto Bressan} } @article {2004, title = {Stability rates for patchy vector fields}, journal = {ESAIM COCV 10 (2004) 168-200}, number = {arXiv.org;math/0111109v1}, year = {2004}, publisher = {EDP Sciences}, abstract = {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.}, doi = {10.1051/cocv:2004003}, url = {http://hdl.handle.net/1963/2959}, author = {Fabio Ancona and Alberto Bressan} } @article {2004, title = {Superlocalization formulas and supersymmetric Yang-Mills theories}, journal = {Nucl. Phys. B 678 (2004) 638-655}, number = {arXiv.org;math-ph/0310036v1}, year = {2004}, publisher = {Elsevier}, abstract = {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.}, doi = {10.1016/j.nuclphysb.2003.11.033}, url = {http://hdl.handle.net/1963/2886}, author = {Ugo Bruzzo and Francesco Fucito} } @article {Bertola:JPA, title = {Second and third order observables of the two-matrix model}, journal = {J. High Energy Phys.}, number = {11}, year = {2003}, pages = {062, 30 pp. (electronic)}, issn = {1126-6708}, author = {Marco Bertola} } @article {2003, title = {Separation of variables for Bi-Hamiltonian systems}, journal = {Math. Phys. Anal. Geom. 6 (2003) 139-179}, number = {SISSA;27/2002/FM}, year = {2003}, publisher = {SISSA Library}, abstract = {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.}, doi = {10.1023/A:1024080315471}, url = {http://hdl.handle.net/1963/1598}, author = {Gregorio Falqui and Marco Pedroni} } @article {2003, title = {Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems}, journal = {SIAM J. Math. Anal. 35 (2003) 759-805}, number = {SISSA;60/2001/M}, year = {2003}, publisher = {SIAM}, abstract = {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.}, doi = {10.1137/S0036141001395388}, url = {http://hdl.handle.net/1963/3071}, author = {Massimiliano Morini} } @mastersthesis {2003, title = {Single-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem}, year = {2003}, school = {SISSA}, url = {http://hdl.handle.net/1963/5342}, author = {Mario Sigalotti} } @article {2003, title = {Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I}, journal = {Comm. Math. Phys. 235 (2003) no.3, 427-466}, number = {SISSA;63/2002/M}, year = {2003}, publisher = {Springer}, doi = {10.1007/s00220-003-0811-y}, url = {http://hdl.handle.net/1963/1633}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @article {2003, title = {Some results on the boundary control of systems of conservation laws}, journal = {SIAM J.Control Optim. 41 (2003),no.2, 607}, number = {SISSA;44/2002/M}, year = {2003}, publisher = {SISSA Library}, doi = {10.1137/S0363012901392529}, url = {http://hdl.handle.net/1963/1615}, author = {Alberto Bressan and Fabio Ancona and Giuseppe Maria Coclite} } @article {2003, title = {Space-adiabatic perturbation theory}, journal = {Adv. Theor. Math. Phys. 7 (2003) 145-204}, number = {arXiv.org;math-ph/0201055v3}, year = {2003}, publisher = {International Press}, abstract = {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 {\textquoteleft}{\textquoteleft}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.}, url = {http://hdl.handle.net/1963/3041}, author = {Gianluca Panati and Herbert Spohn and Stefan Teufel} } @article {2003, title = {A stability result for nonlinear Neumann problems under boundary variations}, journal = {J.Math. Pures Appl. (9) 82 (2003) no.5 , 503}, number = {SISSA;48/2002/M}, year = {2003}, publisher = {SISSA Library}, abstract = {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.}, doi = {10.1016/S0021-7824(03)00014-X}, url = {http://hdl.handle.net/1963/1618}, author = {Gianni Dal Maso and Francois Ebobisse and Marcello Ponsiglione} } @article {2002, title = {The scalar curvature problem on $S\\\\sp n$: an approach via Morse theory}, journal = {Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445}, number = {SISSA;117/99/M}, year = {2002}, publisher = {Springer}, doi = {10.1007/s005260100110}, url = {http://hdl.handle.net/1963/1331}, author = {Andrea Malchiodi} } @article {2002, title = {Singular elliptic problems with critical growth}, journal = {Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876}, number = {SISSA;54/99/M}, year = {2002}, publisher = {Dekker}, doi = {10.1081/PDE-120004887}, url = {http://hdl.handle.net/1963/1268}, author = {Paolo Caldiroli and Andrea Malchiodi} } @article {2002, title = {Solutions concentrating on spheres to symmetric singularly perturbed problems}, journal = {C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150}, number = {SISSA;23/2002/M}, year = {2002}, publisher = {SISSA Library}, abstract = {We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere.}, doi = {10.1016/S1631-073X(02)02414-7}, url = {http://hdl.handle.net/1963/1594}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @mastersthesis {2002, title = {Space-adiabatic Decoupling in Quantum Dynamics}, year = {2002}, school = {SISSA}, url = {http://hdl.handle.net/1963/6360}, author = {Gianluca Panati} } @article {2002, title = {Space-adiabatic perturbation theory in quantum dynamics}, journal = {Physical review letters. 2002 Jun; 88(25 Pt 1):250405}, number = {PMID:12097080;}, year = {2002}, publisher = {American Physical Society}, abstract = {A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schr{\"o}dinger 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.}, doi = {10.1103/PhysRevLett.88.250405}, url = {http://hdl.handle.net/1963/5985}, author = {Gianluca Panati and Herbert Spohn and Stefan Teufel} } @article {2002, title = {Stability of planar switched systems: the linear single input case}, journal = {SIAM J. Control Optim. 41 (2002), no. 1, 89-112}, number = {SISSA;72/00/M}, year = {2002}, publisher = {SIAM}, abstract = {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 {\texttimes} 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.}, doi = {10.1137/S0363012900382837}, url = {http://hdl.handle.net/1963/1529}, author = {Ugo Boscain} } @article {2002, title = {On the Stability of the Standard Riemann Semigroup}, journal = {P. Am. Math. Soc., 2002, 130, 1961}, number = {SISSA;71/00/M}, year = {2002}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1528}, author = {Stefano Bianchini and Rinaldo M. Colombo} } @inbook {2001, title = {S^2 type parametric surfaces with prescribed mean curvature and minimal energy}, booktitle = {Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkh{\"a}user, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77}, number = {SISSA;34/2002/M}, year = {2001}, publisher = {Birkhauser}, organization = {Birkhauser}, url = {http://hdl.handle.net/1963/1605}, author = {Paolo Caldiroli and Roberta Musina} } @article {2001, title = {On the spreading of characteristics for non-convex conservation laws}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925}, year = {2001}, publisher = {Cambridge University Press}, abstract = {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 H{\"o}lder 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.}, doi = {10.1017/S0308210500001189}, url = {http://hdl.handle.net/1963/3265}, author = {Helge Kristian Jenssen and Carlo Sinestrari} } @article {2001, title = {Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions}, journal = {Siam J. Math. Anal., 2001, 33, 959}, number = {SISSA;65/00/M}, year = {2001}, publisher = {SISSA Library}, abstract = {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.}, doi = {10.1137/S0036141000377900}, url = {http://hdl.handle.net/1963/1523}, author = {Stefano Bianchini} } @article {2001, title = {Stationary states for a two-dimensional singular Schrodinger equation}, journal = {Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633.}, number = {SISSA;35/99/M}, year = {2001}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1249}, author = {Paolo Caldiroli and Roberta Musina} } @article {2001, title = {On the subanalyticity of Carnot-Caratheodory distances}, journal = {Ann. I. H. Poincare - An., 2001, 18, 359}, number = {SISSA;25/00/M}, year = {2001}, publisher = {SISSA Library}, doi = {10.1016/S0294-1449(00)00064-0}, url = {http://hdl.handle.net/1963/1483}, author = {Andrei A. Agrachev and Jean-Paul Gauthier} } @article {2001, title = {On the symmetric scalar curvature problem on S\\\\sp n}, journal = {J. Differential Equations 170 (2001) 228-245}, year = {2001}, publisher = {Elsevier}, abstract = {We discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries.}, doi = {10.1006/jdeq.2000.3816}, url = {http://hdl.handle.net/1963/3095}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @article {2000, title = {Scalar curvature under boundary conditions}, journal = {Cr. Acad. Sci. I-Math, 2000, 330, 1013}, number = {SISSA;48/00/M}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0764-4442(00)00312-8}, url = {http://hdl.handle.net/1963/1506}, author = {Antonio Ambrosetti and Li YanYan and Andrea Malchiodi} } @article {2000, title = {The semigroup generated by a Temple class system with non-convex flux function}, journal = {Differential Integral Equations 13 (2000) 1529-1550}, number = {SISSA;107/98/M}, year = {2000}, publisher = {Khayyam Publishing}, abstract = {We consider the Cauchy problem for a nonlinear n {\texttimes} 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.}, url = {http://hdl.handle.net/1963/3221}, author = {Stefano Bianchini} } @article {2000, title = {On the shift differentiability of the flow generated by a hyperbolic system of conservation laws}, journal = {Discrete Contin. Dynam. Systems 6 (2000), no. 2, 329-350}, number = {SISSA;60/99/M}, year = {2000}, publisher = {American Institute of Mathematical Sciences}, doi = {10.3934/dcds.2000.6.329}, url = {http://hdl.handle.net/1963/1274}, author = {Stefano Bianchini} } @article {2000, title = {Some Properties of Non-linear sigma-Models in Noncommutative Geometry}, journal = {Int. J. Mod. Phys. B 14 (2000) 2367-2382}, number = {SISSA;158/99/FM}, year = {2000}, publisher = {SISSA Library}, abstract = {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.}, doi = {10.1142/S0217979200001898}, url = {http://hdl.handle.net/1963/1373}, author = {Ludwik Dabrowski and Thomas Krajewski and Giovanni Landi} } @article {2000, title = {Stability of L^infty Solutions of Temple Class Systems}, journal = {Differential Integral Equations 13 (2000) 1503-1528}, number = {SISSA;134/98/M}, year = {2000}, publisher = {Khayyam Publishing}, abstract = {Let $u_t+f(u)_x=0$ 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.

}, url = {http://hdl.handle.net/1963/3256}, author = {Alberto Bressan and Paola Goatin} } @article {2000, title = {On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature}, number = {SISSA;102/00/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1558}, author = {Roberta Musina and Paolo Caldiroli} } @inbook {2000, title = {Stokes Matrices for Frobenius Manifolds and the 6 Painlev{\'e} Equation}, booktitle = {Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109}, number = {Rokko lectures in mathematics;vol. 7}, year = {2000}, publisher = {Kobe University, Japan}, organization = {Kobe University, Japan}, abstract = {These notes are a short review on the theory of Frobenius manifolds and its connection to problems of isomonodromy deformations and to Painlev{\textquoteright}e equations.}, keywords = {Painlev{\'e} equation}, isbn = {4-907719-07-8}, url = {http://hdl.handle.net/1963/6546}, author = {Davide Guzzetti} } @article {2000, title = {Super KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy}, journal = {J. Geom. Phys. 35 (2000), no. 2-3, 239-272}, number = {SISSA;152/99/FM}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0393-0440(00)00007-3}, url = {http://hdl.handle.net/1963/1367}, author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa} } @article {1999, title = {On the scalar curvature problem under symmetry}, number = {SISSA;73/99/M}, year = {1999}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1287}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @article {1999, title = {Some properties of the solutions of obstacle problems with measure data}, journal = {Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116}, year = {1999}, url = {http://hdl.handle.net/1963/6432}, author = {Paolo Dall{\textquoteright}Aglio and Gianni Dal Maso} } @article {1999, title = {Stokes matrices and monodromy of the quantum cohomology of projective spaces}, journal = {Comm. Math. Phys. 207 (1999) 341-383}, number = {arXiv.org;math/9904099v1}, year = {1999}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/s002200050729}, url = {http://hdl.handle.net/1963/3475}, author = {Davide Guzzetti} } @article {1999, title = {Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws}, journal = {Indiana Univ. Math. J. 48 (1999), no. 1, 43--84}, number = {SISSA;96/97/M}, year = {1999}, publisher = {Indiana University}, abstract = {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.}, doi = {10.1512/iumj.1999.48.1524}, url = {http://hdl.handle.net/1963/3374}, author = {Alberto Bressan and Philippe G. LeFloch} } @article {1998, title = {Special functions with bounded variation and with weakly differentiable traces on the jump set}, journal = {NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243}, number = {SISSA;123/95/M}, year = {1998}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1025}, author = {Luigi Ambrosio and Andrea Braides and Adriana Garroni} } @article {1997, title = {The semigroup generated by a temple class system with large data}, journal = {Differential Integral Equations 10 (1997), no. 3, 401-418}, number = {SISSA;121/95/M}, year = {1997}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/1023}, author = {Paolo Baiti and Alberto Bressan} } @article {1997, title = {Shift-differentiability of the flow generated by a conservation law}, journal = {Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58.}, number = {SISSA;131/95/M}, year = {1997}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/1033}, author = {Alberto Bressan and Graziano Guerra} } @mastersthesis {1997, title = {Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains}, year = {1997}, school = {SISSA}, keywords = {Dirichlet problems}, url = {http://hdl.handle.net/1963/5698}, author = {Rodica Toader} } @article {1997, title = {Some properties of reachable solutions of nonlinear elliptic equations with measure data}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. S{\'e}r. 4, 25 no. 1-2 (1997), p. 375-396}, year = {1997}, publisher = {SISSA}, url = {http://hdl.handle.net/1963/6434}, author = {Gianni Dal Maso and Annalisa Malusa} } @article {1997, title = {Statistics in space dimension two}, journal = {Lett. Math. Phys. 40 (1997), no. 3, 235-256}, number = {SISSA;5/96/ILAS/FM}, year = {1997}, publisher = {SISSA Library}, abstract = {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).}, doi = {10.1023/A:1007361832622}, url = {http://hdl.handle.net/1963/130}, author = {Gianfausto Dell{\textquoteright}Antonio and Rodolfo Figari and Alessandro Teta} } @article {1997, title = {Structural stability for time-optimal planar sytheses}, journal = {Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371}, number = {SISSA;95/95/M}, year = {1997}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/997}, author = {Alberto Bressan and Benedetto Piccoli} } @article {1996, title = {The semigroup approach to systems of conservation laws}, journal = {Mat. Contemp. 10 (1996) 21-74}, number = {SISSA;135/95/M}, year = {1996}, publisher = {Sociedade Brasileira de Matematica}, url = {http://hdl.handle.net/1963/1037}, author = {Alberto Bressan} } @article {1996, title = {Solving Honig generic problem about Volterra integral equations}, journal = {Bull. Polish Acad. Sci. Math. 44 (1996), no. 4, 495--498}, number = {SISSA;38/95/M}, year = {1996}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/941}, author = {Giovanni Vidossich} } @article {1995, title = {Some control problems for the pendulum}, journal = {Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318}, number = {SISSA;80/95/M}, year = {1995}, publisher = {IEEE}, abstract = {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.}, doi = {10.1109/CDC.1995.478998}, url = {http://hdl.handle.net/1963/982}, author = {Benedetto Piccoli} } @article {1995, title = {Special functions of bounded deformation}, number = {SISSA;76/95/M}, year = {1995}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/978}, author = {Giovanni Bellettini and Alessandra Coscia and Gianni Dal Maso} } @mastersthesis {1992, title = {Some Problems in the Calculus of the Variations}, year = {1992}, school = {SISSA}, keywords = {Calculus of variations}, url = {http://hdl.handle.net/1963/5428}, author = {Sandro Zagatti} } @article {1991, title = {Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions}, journal = {Appl.Math.Optim. 23 (1991), no.1, p. 17-49.}, number = {SISSA;124/89/M}, year = {1991}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/880}, author = {Giuseppe Buttazzo and Gianni Dal Maso} } @article {1991, title = {On systems of ordinary differential equations with measures as controls}, journal = {Differential Integral Equations 4 (1991), no.4, p.739-765.}, number = {SISSA;82/89/M}, year = {1991}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/840}, author = {Gianni Dal Maso and Franco Rampazzo} } @article {1990, title = {Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions}, journal = {Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535.}, number = {SISSA;49/89/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/809}, author = {Giuseppe Buttazzo and Gianni Dal Maso} } @mastersthesis {1989, title = {Singular perturbation of the Laplacian and connections with models of random media}, year = {1989}, school = {SISSA}, url = {http://hdl.handle.net/1963/6348}, author = {Alessandro Teta} } @article {1989, title = {On the solvability of boundary value problems for higher order ordinary differential equations (Revised version)}, journal = {Nonlinear Anal. 13 (1989), no. 10, 1171-1179}, number = {SISSA;66/88/M}, year = {1989}, publisher = {SISSA Library}, doi = {10.1016/0362-546X(89)90005-9}, url = {http://hdl.handle.net/1963/662}, author = {Giovanni Vidossich} } @article {1989, title = {On the solvability of boundary value problems for higher order ordinary differential equations}, journal = {Nonlinear Anal. 13 (1989), no. 10, 1171-179}, number = {SISSA;35/88/M}, year = {1989}, publisher = {SISSA Library}, doi = {10.1016/0362-546X(89)90005-9}, url = {http://hdl.handle.net/1963/631}, author = {Giovanni Vidossich} } @article {1989, title = {Surfaces of minimal area enclosing a given body in R\\\\sp 3.}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990).}, number = {SISSA;23/88/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/619}, author = {Giovanni Mancini and Roberta Musina} } @article {1988, title = {Some properties of a class of nonlinear variational $m$-capacities}, journal = {J.Funct.Anal. 79, 1988, no. 2, 476-492}, number = {SISSA;3/87/M}, year = {1988}, publisher = {SISSA Library}, doi = {10.1016/0022-1236(88)90022-5}, url = {http://hdl.handle.net/1963/485}, author = {Gianni Dal Maso and Anneliese Defranceschi} } @article {1988, title = {Susy-curves and supermoduli}, number = {SISSA;169/88/FM}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/761}, author = {Gregorio Falqui and Cesare Reina} } @article {1987, title = {Solutions with minimal period for Hamiltonian systems in a potential well.}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296}, number = {SISSA;79/85/M}, year = {1987}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/466}, author = {Antonio Ambrosetti and Vittorio Coti Zelati} } @article {1987, title = {Symmetry breaking in Hamiltonian systems}, journal = {J. Differential Equations 67 (1987), no. 2, 165-184}, number = {SISSA;22/85/M}, year = {1987}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/409}, author = {Antonio Ambrosetti and Vittorio Coti Zelati and Ivar Ekeland} } @article {1985, title = {Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets}, journal = {J. Funct. Anal. 62 (1985), no. 2, 119--159}, number = {SISSA;15/84/M}, year = {1985}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/318}, author = {Gianni Dal Maso} } @article {1985, title = {Some singular perturbation problems in the calculus of variations.}, journal = {Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985}, number = {SISSA;62/83/M}, year = {1985}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/297}, author = {Gianni Dal Maso} } @mastersthesis {1984, title = {Spin Structures and Global Conformal Transformations}, year = {1984}, school = {SISSA}, keywords = {Spinors}, url = {http://hdl.handle.net/1963/5854}, author = {Ludwik Dabrowski} }