In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

%B QUIET Selected Contributions %I Springer International Publishing %G eng %U https://arxiv.org/abs/1901.02285 %& Non-Intrusive Polynomial Chaos Method Applied to Problems in Computational Fluid Dynamics [...] %0 Journal Article %J Journal of Convex Analysis %D 2020 %T A numerical study of the jerky crack growth in elastoplastic materials with localized plasticity %A Gianni Dal Maso %A Luca Heltai %B Journal of Convex Analysis %G eng %U https://arxiv.org/abs/2004.12705 %0 Journal Article %J JHEP %D 2019 %T N=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts %A Aditya Bawane %A Benvenuti, Sergio %A Giulio Bonelli %A Muteeb, Nouman %A Alessandro Tanzini %B JHEP %V 07 %P 040 %G eng %U http://inspirehep.net/record/1631219/ %R 10.1007/JHEP07(2019)040 %0 Journal Article %J Canadian Mathematical Bulletin %D 2019 %T A Note About the Strong Maximum Principle on RCD Spaces %A Nicola Gigli %A Chiara Rigoni %XWe give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

%B Canadian Mathematical Bulletin %I Canadian Mathematical Society %V 62 %P 259–266 %G eng %R 10.4153/CMB-2018-022-9 %0 Journal Article %J Discrete & Computational Geometry %D 2019 %T On the Number of Flats Tangent to Convex Hypersurfaces in Random Position %A Khazhgali Kozhasov %A Antonio Lerario %B Discrete & Computational Geometry %8 Mar %G eng %U https://doi.org/10.1007/s00454-019-00067-0 %R 10.1007/s00454-019-00067-0 %0 Journal Article %J Journal of the Mechanics and Physics of Solids %D 2019 %T Nutations in growing plant shoots: The role of elastic deformations due to gravity loading %A Daniele Agostinelli %A Alessandro Lucantonio %A Giovanni Noselli %A Antonio DeSimone %K Circumnutations %K Flutter instability %K Gravitropism %K Hopf bifurcation %XThe effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

%B Journal of the Mechanics and Physics of Solids %P 103702 %G eng %U https://doi.org/10.1016/j.jmps.2019.103702 %R 10.1016/j.jmps.2019.103702 %0 Journal Article %J Comm. Math. Phys %D 2018 %T Noncommutative Painlevé Equations and Systems of Calogero Type %A Marco Bertola %A Mattia Cafasso %A V. Rubtsov %B Comm. Math. Phys %G eng %0 Report %D 2018 %T Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis %A Alessandro Michelangeli %A Giuseppe Pitton %X We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. %G en %U http://preprints.sissa.it/handle/1963/35323 %1 35633 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-09-20T06:04:10Z No. of bitstreams: 1 SISSA_preprint_35-2018-MATE.pdf: 2536075 bytes, checksum: 323dca7431103028ecadfc71c052f4ed (MD5) %0 Report %D 2018 %T On the notion of parallel transport on RCD spaces %A Nicola Gigli %A Enrico Pasqualetto %G eng %0 Journal Article %D 2018 %T A novel reduced order model for vortex induced vibrations of long flexible cylinders %A Giovanni Stabile %A Hermann G. Matthies %A Claudio Borri %I Elsevier {BV} %V 156 %P 191–207 %8 may %G eng %U https://doi.org/10.1016/j.oceaneng.2018.02.064 %R 10.1016/j.oceaneng.2018.02.064 %0 Journal Article %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2018 %T Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves %A Tamara Grava %A Christian Klein %A Giuseppe Pitton %XA detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 474 %P 20170458 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0458 %R 10.1098/rspa.2017.0458 %0 Journal Article %J COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING %D 2018 %T NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces %A Giuseppe Pitton %A Luca Heltai %B COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING %V 338 %P 440–462 %G eng %U https://arxiv.org/abs/1804.08271 %R 10.1016/j.cma.2018.04.039 %0 Journal Article %J COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING %D 2017 %T A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling %A Luca Heltai %A Kiendl, J. %A Antonio DeSimone %A Alessandro Reali %B COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING %V 316 %P 522–546 %G eng %U http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H %R 10.1016/j.cma.2016.08.008 %0 Journal Article %J Ann. Mat. Pura Appl. %D 2017 %T A note on a fixed point theorem on topological cylinders %A Guglielmo Feltrin %XWe present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel’skii ones.

%B Ann. Mat. Pura Appl. %I Springer Verlag %G en %U http://urania.sissa.it/xmlui/handle/1963/35263 %1 35567 %2 Mathematics %4 1 %# MAT/05 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2016-11-21T07:45:03Z (GMT) No. of bitstreams: 0 %R 10.1007/s10231-016-0623-2 %0 Journal Article %J Journal of Dynamics and Differential Equations %D 2017 %T A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations %A Lorenzo Nardini %B Journal of Dynamics and Differential Equations %V 29 %P 783–797 %8 Jun %G eng %U https://doi.org/10.1007/s10884-015-9461-y %R 10.1007/s10884-015-9461-y %0 Journal Article %J Biomechanics and Modeling in Mechanobiology %D 2017 %T Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts %A Francesco Ballarin %A Elena Faggiano %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %A Sonia Ippolito %A Roberto Scrofani %B Biomechanics and Modeling in Mechanobiology %V 16 %P 1373-1399 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851&doi=10.1007%2fs10237-017-0893-7&partnerID=40&md5=c388f20bd5de14187bad9ed7d9affbd0 %R 10.1007/s10237-017-0893-7 %0 Journal Article %J Rend. Sem. Mat. Univ. Padova %D 2016 %T New existence results for the mean field equation on compact surfaces via degree theory %A Aleks Jevnikar %B Rend. Sem. Mat. Univ. Padova %V 136 %P 11–17 %G eng %R 10.4171/RSMUP/136-2 %0 Report %D 2016 %T Non-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics %A Alessandro Michelangeli %A Giuseppe Pitton %X We present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time. %G en %U http://urania.sissa.it/xmlui/handle/1963/35266 %1 35572 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-16T12:09:24Z No. of bitstreams: 1 SISSA_preprint_63-2016-MATE_Michelangeli-Pitton-2016.pdf: 6158349 bytes, checksum: ab11de2762ff510e6833474d0688a8b4 (MD5) %0 Journal Article %J Advanced Nonlinear Studies %D 2016 %T A note on a multiplicity result for the mean field equation on compact surfaces %A Aleks Jevnikar %B Advanced Nonlinear Studies %I De Gruyter %V 16 %P 221–229 %G eng %R 10.1515/ans-2015-5009 %0 Journal Article %J Journal of High Energy Physics %D 2015 %T N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity %A Aditya Bawane %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %XWe consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2 \times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

%B Journal of High Energy Physics %V 2015 %P 54 %8 Jul %G eng %U https://doi.org/10.1007/JHEP07(2015)054 %R 10.1007/JHEP07(2015)054 %0 Thesis %D 2015 %T Normal matrix models and orthogonal polynomials for a class of potentials with discrete rotational symmetries %A Dario Merzi %K Mathematical Physics %X In this thesis we are going to study normal random matrix models which generalize naturally the polynomially perturbed Ginibre ensamble, focusing in particular on their eigenvalue distribution and on the asymptotics of the associated orthogonal polynomials. \\ The main result we are going to present are the following: \begin{itemize} \item we describe the explicit derivation of the equilibrium measure for a class of potentials with discrete rotational symmetries, namely of the form \[V(z)=|z|^{2n}-t(z^{d}+\bar{z}^{d})\qquad n,d\in\mathbb{N},\ \ d\leq2n\ \ t>0 .\] \item We obtain the strong asymptotics for the orthogonal polynomials associated to the weight \[ e^{-NV(z)},\quad V(z)=|z|^{2s}-t(z^s+\bar{z}^{s}) \qquad z \in \mathbb{C},\;s\in \mathbb{N},\quad t>0,\] and we will show how the density of their zeroes is related to the eigenvalue distribution of the corresponding matrix model; \item We show how the conformal maps used to describe the support of the equilibrium measure for polynomial perturbation of the potential $V(z)=|z|^{2n}$ lead to a natural generalization of the concept of polynomial curves introduced in by Elbau. \end{itemize} %I SISSA %G en %1 34938 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Dario Merzi (dmerzi@sissa.it) on 2015-10-24T00:25:34Z No. of bitstreams: 1 Tesi.pdf: 2303697 bytes, checksum: 620bce2fe472d72e2a7050687b21dc08 (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. %D 2015 %T A note on compactness properties of the singular Toda system %A Luca Battaglia %A Gabriele Mancini %XIn this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

%B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. %V 26 %P 299-307 %G en %1 34669 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-07T16:01:01Z No. of bitstreams: 1 art3.pdf: 146803 bytes, checksum: 362923e2dd63f86658dd3bb0701ce05b (MD5) %R 10.4171/RLM/708 %0 Journal Article %D 2014 %T N = 2 Quiver Gauge Theories on A-type ALE Spaces %A Ugo Bruzzo %A Francesco Sala %A Richard J. Szabo %X We survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in N = 2 gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity C2/Zk, in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic N = 2 superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg–Witten geometry. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34719 %1 34918 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-22T12:43:35Z No. of bitstreams: 1 preprint2014.pdf: 715288 bytes, checksum: aa2d57d1d2ee3b6602bdcef73696035c (MD5) %R 10.1007/s11005-014-0734-x %0 Journal Article %D 2014 %T New results on Gamma-limits of integral functionals %A Nadia Ansini %A Gianni Dal Maso %A Caterina Ida Zeppieri %K Gamma-convergence %I Elsevier %G en %U http://hdl.handle.net/1963/5880 %1 5745 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T12:48:08Z No. of bitstreams: 1 03M_2012_Ansini.pdf: 262251 bytes, checksum: 4e0dd5c07ab75bd2da8aa462f2ae8f0f (MD5) %R 10.1016/j.anihpc.2013.02.005 %0 Thesis %D 2014 %T Non-commutative integration for spectral triples associated to quantum groups %A Marco Matassa %K Non-commutative geometry %X This thesis is dedicated to the study of non-commutative integration, in the sense of spectral triples, for some non-commutative spaces associated to quantum groups. %I SISSA %G en %1 7363 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Marco Matassa (mmatassa@sissa.it) on 2014-04-28T08:04:56Z No. of bitstreams: 1 Thesis (with corrections).pdf: 1129467 bytes, checksum: 77aa801082828a7b5b3fc10070f06319 (MD5) %0 Journal Article %D 2014 %T Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D %A Luca Heltai %A Marino Arroyo %A Antonio DeSimone %K Isogeometric Analysis %X Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM. %I Elsevier %G en %U http://hdl.handle.net/1963/6326 %1 6250 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-12-03T08:19:28Z No. of bitstreams: 1 isogeo_stokes.pdf: 732320 bytes, checksum: 224ef57de6c49f03db0afaccdcb234f9 (MD5) %R 10.1016/j.cma.2013.09.017 %0 Report %D 2013 %T N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %A Futoshi Yagi %X We compute the Nekrasov partition function of gauge theories on the\r\n(resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We\r\ndiscuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2\r\n\\to 0 limit along with its modular properties and how to derive them from the\r\nM-theory perspective. On the two-dimensional conformal field theory side, our\r\nresults can be interpreted in terms of representations of the direct sum of\r\nHeisenberg plus W_N-algebrae with suitable central charges, which can be\r\ncomputed from the fan of the resolved toric variety.We provide a check of this\r\ncorrespondence by computing the central charge of the two-dimensional theory\r\nfrom the anomaly polynomial of M5-brane theory. Upon using the AGT\r\ncorrespondence our results provide a candidate for the conformal blocks and\r\nthree-point functions of a class of the two-dimensional CFTs which includes\r\nparafermionic theories. %I SISSA %G en %U http://hdl.handle.net/1963/6577 %1 6522 %2 Mathematics %4 -1 %$ Submitted by Alessandro Tanzini (tanzini@sissa.it) on 2013-04-04T10:00:01Z\nNo. of bitstreams: 1\n1208.0790v4.pdf: 372527 bytes, checksum: 5fae7067b646df2fca0b20daa82b5cff (MD5) %0 Journal Article %J Oberwolfach Reports %D 2013 %T A New Quadratic Potential for Scalar Conservation Laws %A Stefano Bianchini %A Stefano Modena %B Oberwolfach Reports %V 29 %G eng %0 Journal Article %D 2013 %T Nonabelian Lie algebroid extensions %A Ugo Bruzzo %A Igor Mencattini %A Pietro Tortella %A Vladimir Rubtsov %K Lie algebroids, nonabelian extensions, spectral sequences %XWe classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

%G en %1 7293 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Ugo Bruzzo (bruzzo@sissa.it) on 2014-02-14T14:16:47Z No. of bitstreams: 1 nonabelian-9.pdf: 401046 bytes, checksum: 3ebfee7dd06925fea31100611bc7e2ca (MD5) %0 Journal Article %J Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130 %D 2013 %T Noncommutative circle bundles and new Dirac operators %A Ludwik Dabrowski %A Andrzej Sitarz %K Quantum principal bundles %X We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection. %B Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130 %I Springer %G en %U http://hdl.handle.net/1963/7384 %1 7432 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-18T10:06:43Z No. of bitstreams: 1 1012.3055v2.pdf: 181206 bytes, checksum: be182e0f568384847efe0f656a70634b (MD5) %R 10.1007/s00220-012-1550-8 %0 Journal Article %J Geometry Partial Differential Equations – proceedings, CRM Series (15), 2013. %D 2013 %T The nonlinear multidomain model: a new formal asymptotic analysis. %A Stefano Amato %A Giovanni Bellettini %A Maurizio Paolini %K bidomain model, anisotropic mean curvature, star-shaped combination %XWe study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

%B Geometry Partial Differential Equations – proceedings, CRM Series (15), 2013. %@ 8876424724 %G en %1 7259 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Stefano Amato (samato@sissa.it) on 2013-11-29T15:38:34Z No. of bitstreams: 1 bidomain_gen.pdf: 320909 bytes, checksum: a47cfa6c6dec3318d5d75f8a6a4a425b (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437–450 %D 2013 %T A note on KAM theory for quasi-linear and fully nonlinear forced KdV %A P Baldi %A Massimiliano Berti %A Riccardo Montalto %K KAM for PDEs %X We present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437–450 %I European Mathematical Society %G en %1 7268 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-12-09T08:16:04Z No. of bitstreams: 1 Baldi-Berti-Montalto-Lincei-Note-KAM-forced-KdV.pdf: 322654 bytes, checksum: ddae153eff7ad17e2be36cb3ba1af9bf (MD5) %R 10.4171/RLM/660 %0 Journal Article %D 2013 %T A note on non-homogeneous hyperbolic operators with low-regularity coefficients %A Ferruccio Colombini %A Francesco Fanelli %XIn this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

%G eng %0 Journal Article %J Math. Models Methods Appl. Sci. 22, 1150016 (2012) %D 2012 %T Nonlinear thin-walled beams with a rectangular cross-section-Part I %A Lorenzo Freddi %A Maria Giovanna Mora %A Roberto Paroni %X Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results. %B Math. Models Methods Appl. Sci. 22, 1150016 (2012) %I World Scientific %G en_US %U http://hdl.handle.net/1963/4104 %1 300 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-17T08:45:48Z\\r\\nNo. of bitstreams: 1\\r\\nFreddi_79M.pdf: 331698 bytes, checksum: 3b0d6e3d51984a8e8222753a57064ee9 (MD5) %R 10.1142/S0218202511500163 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2012 %T A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem %A Andrea Sfecci %K Neumann problem %K Nonresonance %K Radial solutions %K Time-map %XWe prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

%B Nonlinear Analysis: Theory, Methods & Applications %V 75 %P 6191 - 6202 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X12002659 %R https://doi.org/10.1016/j.na.2012.06.023 %0 Journal Article %J Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37 %D 2012 %T Non-uniqueness results for critical metrics of regularized determinants in four dimensions %A Matthew Gursky %A Andrea Malchiodi %X The regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger's half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions. %B Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37 %I Springer %G en %U http://hdl.handle.net/1963/6559 %1 6488 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:25:46Z No. of bitstreams: 1 1105.3762v3.pdf: 658857 bytes, checksum: 2821cb9caed2f5cda3b406c745b73009 (MD5) %R 10.1007/s00220-012-1535-7 %0 Journal Article %J Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 %D 2012 %T Numerical modelling of installation effects for diaphragm walls in sand %A Riccardo Conti %A Luca de Sanctis %A Giulia M.B. Viggiani %K Constitutive relations %X The scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic. %B Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 %I Springer %G en %U http://hdl.handle.net/1963/6934 %1 6916 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-05-30T10:23:32Z No. of bitstreams: 0 %R 10.1007/s11440-011-0157-0 %0 Journal Article %J Physica D 241, nr. 23-24 (2012): 2246-2264 %D 2012 %T Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions %A Tamara Grava %A Christian Klein %K Korteweg-de Vries equation %X We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically. %B Physica D 241, nr. 23-24 (2012): 2246-2264 %I Elsevier %G en %1 7069 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-09-16T14:49:23Z No. of bitstreams: 1 1202.0962v2.pdf: 2652650 bytes, checksum: d8678338138745b35d8515af39f85d18 (MD5) %R 10.1016/j.physd.2012.04.001 %0 Journal Article %J Geometric and Functional Analysis 21 (2011) 1196-1217 %D 2011 %T New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces %A Andrea Malchiodi %A David Ruiz %X We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results. %B Geometric and Functional Analysis 21 (2011) 1196-1217 %I Springer %G en_US %U http://hdl.handle.net/1963/4099 %1 305 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-11-10T10:27:54Z\\r\\nNo. of bitstreams: 1\\r\\nMalchiodi-Ruiz-74M.pdf: 192985 bytes, checksum: 61acb10ab3cde055824228920d16987a (MD5) %R 10.1007/s00039-011-0134-7 %0 Journal Article %J Advanced Nonlinear Studies %D 2011 %T Nonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions %A Alessandro Fonda %A Maurizio Garrione %XWe show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

%B Advanced Nonlinear Studies %I Advanced Nonlinear Studies, Inc. %V 11 %P 391–404 %G eng %R 10.1515/ans-2011-0209 %0 Report %D 2011 %T Nonlinear thin-walled beams with a rectangular cross-section - Part II %A Lorenzo Freddi %A Maria Giovanna Mora %A Roberto Paroni %K Thin-walled cross-section beams %X In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section.. %I SISSA %G en %U http://hdl.handle.net/1963/4169 %1 3891 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-20T13:52:25Z\\nNo. of bitstreams: 1\\nFreddi_Mora_14_M.pdf: 427788 bytes, checksum: e3682dceada2647cc7dee99102979180 (MD5) %0 Journal Article %J Duke Mathematical Journal %D 2011 %T Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces %A Massimiliano Berti %A Michela Procesi %X We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr¨odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions. %B Duke Mathematical Journal %V 159 %8 2011 %G eng %N 3 %& 479 %R 10.1215/00127094-1433403 %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2011 %T A note on a superlinear indefinite Neumann problem with multiple positive solutions %A Alberto Boscaggin %K Indefinite weight %K Nonlinear boundary value problems %K positive solutions %K Shooting method %XWe prove the existence of three positive solutions for the Neumann problem associated to u″+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta−(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.

%B Journal of Mathematical Analysis and Applications %V 377 %P 259 - 268 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022247X10008796 %R https://doi.org/10.1016/j.jmaa.2010.10.042 %0 Journal Article %J J. Phys. A 44 (2011) 315302 %D 2011 %T On the number of eigenvalues of a model operator related to a system of three particles on lattices %A Gianfausto Dell'Antonio %A Zahriddin I. Muminov %A Y.M. Shermatova %B J. Phys. A 44 (2011) 315302 %I IOP Publishing %G en %U http://hdl.handle.net/1963/5496 %1 5340 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-16T07:58:53Z\\nNo. of bitstreams: 0 %] We consider a quantum mechanical system on a lattice \\\\mathbb {Z}^3 in which three particles, two of them being identical, interact through a zero-range potential. We admit a very general form for the \\\'kinetic\\\' part H0γ of the Hamiltonian, which contains a parameter γ to distinguish the two identical particles from the third one (in the continuum case this parameter would be the inverse of the mass). We prove that there is a value γ* of the parameter such that only for γ < γ* the Efimov effect (infinite number of bound states if the two-body interactions have a resonance) is absent for the sector of the Hilbert space which contains functions which are antisymmetric with respect to the two identical particles, while it is present for all values of γ on the symmetric sector. We comment briefly on the relation of this result with previous investigations on the Thomas effect. We also establish the following asymptotics for the number N(z) of eigenvalues z below Emin, the lower limit of the essential spectrum of H0. In the symmetric subspace \\\\lim _{z \\\\rightarrow E_{\\\\rm min}^- } { N^s(z) \\\\over | \\\\log | E_{\\\\rm min} -z| | } = \\\\mathcal {U}_0^s (\\\\gamma ), \\\\quad \\\\forall\\\\ \\\\gamma, whereas in the antisymmetric subspace \\\\lim _{z \\\\rightarrow E_{\\\\rm min}^- } { N^{as}(z) \\\\over | \\\\log | E_{\\\\rm min} -z| | } = \\\\mathcal {U}_0^{as} (\\\\gamma ), \\\\quad \\\\forall\\\\ \\\\gamma \\\\gt \\\\gamma ^*, where \\\\mathcal {U}_0^{ as } (\\\\gamma ), \\\\mathcal {U}_0^s (\\\\gamma ) are written explicitly as a function of the integral kernel of operators acting on L^2((0,r) \\\\times (L^2 (\\\\mathbb {S}^2) \\\\otimes L^2 (\\\\mathbb {S}^2)) (\\\\mathbb {S}^2 is the unit sphere in \\\\mathbb {R}^3). %R 10.1088/1751-8113/44/31/315302 %0 Journal Article %J Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %D 2011 %T Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers %A François Alouges %A Antonio DeSimone %A Luca Heltai %K Optimal swimming %X We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms. %B Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3657 %1 648 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-23T17:30:51Z\\r\\nNo. of bitstreams: 1\\r\\nSissa33_2009M.pdf: 708341 bytes, checksum: 6134bd52f083488620fb5bb24bcf9b93 (MD5) %R 10.1142/S0218202511005088 %0 Journal Article %J SIAM J. Appl. Math. 71 (2011) 983-1008 %D 2011 %T Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations %A Boris Dubrovin %A Tamara Grava %A Christian Klein %X This article is concerned with a conjecture in [B. Dubrovin, Comm. Math. Phys., 267 (2006), pp. 117–139] on the formation of dispersive shocks in a class of Hamiltonian dispersive regularizations of the quasi-linear transport equation. The regularizations are characterized by two arbitrary functions of one variable, where the condition of integrability implies that one of these functions must not vanish. It is shown numerically for a large class of equations that the local behavior of their solution near the point of gradient catastrophe for the transport equation is described by a special solution of a Painlevé-type equation. This local description holds also for solutions to equations where blowup can occur in finite time. Furthermore, it is shown that a solution of the dispersive equations away from the point of gradient catastrophe is approximated by a solution of the transport equation with the same initial data, modulo terms of order $\\\\epsilon^2$, where $\\\\epsilon^2$ is the small dispersion parameter. Corrections up to order $\\\\epsilon^4$ are obtained and tested numerically. %B SIAM J. Appl. Math. 71 (2011) 983-1008 %I SIAM %G en %U http://hdl.handle.net/1963/4951 %1 4732 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-27T12:18:45Z\\nNo. of bitstreams: 1\\n1101.0268v1.pdf: 522533 bytes, checksum: d9e2df220724f918ec3b888cef3593d4 (MD5) %R 10.1137/100819783 %0 Thesis %B Università degli Studi di Trieste and SISSA %D 2010 %T New approximation results for free discontinuity problems %A Flaviana Iurlano %B Università degli Studi di Trieste and SISSA %G eng %9 Master's thesis %0 Journal Article %J Adv. Calc. Var. 3 (2010) 287-319 %D 2010 %T Nonlocal character of the reduced theory of thin films with higher order perturbations %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %B Adv. Calc. Var. 3 (2010) 287-319 %G en_US %U http://hdl.handle.net/1963/3754 %1 563 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-15T09:06:42Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo.pdf: 288658 bytes, checksum: 7815e9376b53eb044b2fb2b57cd49b53 (MD5) %R 10.1515/ACV.2010.012, /July/2010 %0 Journal Article %J arXiv preprint arXiv:1008.5036 %D 2010 %T A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point %A Ugo Boscain %A Grégoire Charlot %A Roberta Ghezzi %B arXiv preprint arXiv:1008.5036 %G eng %0 Report %D 2010 %T On the number of positive solutions of some semilinear elliptic problems %A Antonio Ambrosetti %G en_US %U http://hdl.handle.net/1963/4083 %1 320 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-04T09:32:44Z\\nNo. of bitstreams: 1\\nAmbrosetti_66M_2010.pdf: 141739 bytes, checksum: c56d5c17199fdefcd3d62c0b2da958a1 (MD5) %0 Report %D 2010 %T Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions %A Simonetta Abenda %A Tamara Grava %A Christian Klein %X The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture.... %G en_US %U http://hdl.handle.net/1963/3840 %1 487 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-05T10:20:56Z\\nNo. of bitstreams: 1\\n0909.1020v1.pdf: 613403 bytes, checksum: be892250a6d664faff51d74b323fea67 (MD5) %0 Journal Article %J C. R. Math. 347 (2009) 211-216 %D 2009 %T A nonlinear theory for shells with slowly varying thickness %A Marta Lewicka %A Maria Giovanna Mora %A Mohammad Reza Pakzad %X We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface. %B C. R. Math. 347 (2009) 211-216 %G en_US %U http://hdl.handle.net/1963/2632 %1 1491 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-17T10:05:31Z\\nNo. of bitstreams: 1\\nLew-Mor-Pak-08.pdf: 159399 bytes, checksum: a9f5009829a4633482d74870c6fd22b6 (MD5) %R 10.1016/j.crma.2008.12.017 %0 Journal Article %J J. Funct. Anal. 256 (2009) 2741-2745 %D 2009 %T A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas %A Roberta Musina %B J. Funct. Anal. 256 (2009) 2741-2745 %G en_US %U http://hdl.handle.net/1963/2698 %1 1402 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-25T14:46:48Z\\nNo. of bitstreams: 1\\nMusina_FiTe.pdf: 141073 bytes, checksum: 84d3efccc14d223256f9971f03942f4e (MD5) %R 10.1016/j.jfa.2008.08.009 %0 Journal Article %J Int. Math. Res. Not. vol. 2008, Article ID rnn038 %D 2008 %T Noncommutative families of instantons %A Giovanni Landi %A Chiara Pagani %A Cesare Reina %A Walter van Suijlekom %X We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$. %B Int. Math. Res. Not. vol. 2008, Article ID rnn038 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3417 %1 918 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T09:40:47Z\\nNo. of bitstreams: 1\\n0710.0721v2.pdf: 290960 bytes, checksum: 7203f1e1dd34fd90d8d3201c7b813b44 (MD5) %R 10.1093/imrn/rnn038 %0 Journal Article %J Rev. Math. Phys. 20 (2008) 979-1006 %D 2008 %T The Noncommutative Geometry of the Quantum Projective Plane %A Francesco D'Andrea %A Ludwik Dabrowski %A Giovanni Landi %X We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)). %B Rev. Math. Phys. 20 (2008) 979-1006 %G en_US %U http://hdl.handle.net/1963/2548 %1 1571 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-14T08:17:29Z\\nNo. of bitstreams: 1\\n0712.3401v1.pdf: 305773 bytes, checksum: 85ef21e8ac9485f12064685740331fc2 (MD5) %R 10.1142/S0129055X08003493 %0 Report %D 2008 %T A note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces %A Massimiliano Morini %G en_US %U http://hdl.handle.net/1963/2654 %1 1469 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-12T11:42:20Z\\nNo. of bitstreams: 1\\nchainmor.pdf: 232603 bytes, checksum: 2798c276d92d0d30c48523748c30a163 (MD5) %0 Journal Article %J Proc. R. Soc. A 464 (2008) 733-757 %D 2008 %T Numerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlevé-II equation %A Tamara Grava %A Christian Klein %X The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\e^2$, $\\\\e\\\\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\\\\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\\\\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a multiscale expansion of the solution of KdV in terms of the Hastings-McLeod solution of the Painlev\\\\\\\'e-II equation. We show numerically that the resulting multiscale solution approximates the KdV solution, in the small dispersion limit, to the order $\\\\epsilon^{2/3}$. %B Proc. R. Soc. A 464 (2008) 733-757 %G en_US %U http://hdl.handle.net/1963/2592 %1 1530 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-02-25T15:08:44Z\\nNo. of bitstreams: 1\\n0708.0638v3.pdf: 453744 bytes, checksum: 05291095860df236125f0d9f8c676fbb (MD5) %R 10.1098/rspa.2007.0249 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310 %D 2007 %T Nearly time optimal stabilizing patchy feedbacks %A Fabio Ancona %A Alberto Bressan %X We consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$. %B Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310 %G en_US %U http://hdl.handle.net/1963/2185 %1 2059 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T08:22:02Z\\nNo. of bitstreams: 1\\n0512531v1.pdf: 428805 bytes, checksum: 8eae0ca68a7339938991d987a677d6f9 (MD5) %R 10.1016/j.anihpc.2006.03.010 %0 Journal Article %J J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252 %D 2007 %T Necessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd) %A Giovanni Leoni %A Massimiliano Morini %XIn this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

%B J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252 %G en_US %U http://hdl.handle.net/1963/2037 %1 2159 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T16:39:37Z\\nNo. of bitstreams: 1\\n05-CNA-001.pdf: 331793 bytes, checksum: b6fd9f7cf79aacffa4d60dda74d183a6 (MD5) %R 10.4171/JEMS/78 %0 Report %D 2007 %T A new model for contact angle hysteresis %A Antonio DeSimone %A Natalie Gruenewald %A Felix Otto %X We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence. %B Netw. Heterog. Media 2 (2007) 211-225 %G en_US %U http://hdl.handle.net/1963/1848 %1 2369 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-26T09:50:36Z\\nNo. of bitstreams: 1\\n37-2006M.pdf: 313357 bytes, checksum: ac507409dc660fba3ec468e50c4fe9b1 (MD5) %0 Thesis %D 2007 %T Noncommutative geometry and quantum group symmetries %A Francesco D'Andrea %K Noncommutative geometry %X It is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07], «we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics» . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no `final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world... %I SISSA %G en %U http://hdl.handle.net/1963/5269 %1 5093 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-01-24T08:56:37Z\\nNo. of bitstreams: 1\\nPhD_D\\\'Andrea_Francesco.pdf: 1636959 bytes, checksum: 0d673f9b1d591a36bd4883bedc49422a (MD5) %0 Journal Article %J NoDEA 13 (2007) 713-734 %D 2007 %T On a notion of unilateral slope for the Mumford-Shah functional %A Gianni Dal Maso %A Rodica Toader %X In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional. %B NoDEA 13 (2007) 713-734 %G en_US %U http://hdl.handle.net/1963/2059 %1 2137 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-06T14:02:51Z\\nNo. of bitstreams: 1\\n0410525v1.pdf: 214576 bytes, checksum: 3722f413401cdb51f778a8c15eeebe71 (MD5) %R 10.1007/s00030-006-4054-4 %0 Journal Article %J J. Phys. A 40 (2007) 14819-14842 %D 2007 %T The number of eigenvalues of three-particle Schrödinger operators on lattices %A Sergio Albeverio %A Gianfausto Dell'Antonio %A Saidakhmat N. Lakaev %X We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero. %B J. Phys. A 40 (2007) 14819-14842 %G en_US %U http://hdl.handle.net/1963/2576 %1 1545 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-28T14:20:38Z\\nNo. of bitstreams: 1\\n0703191v1.pdf: 254244 bytes, checksum: a662f118f430d7b424e751fa5f07ed92 (MD5) %R 10.1088/1751-8113/40/49/015 %0 Report %D 2007 %T Numerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations %A Tamara Grava %A Christian Klein %X The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\\\\epsilon$. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. In this manuscript we give a quantitative analysis of the discrepancy between the numerical solution of the KdV equation in the small dispersion limit and the corresponding approximate solution for values of $\\\\epsilon$ between $10^{-1}$ and $10^{-3}$. The numerical results are compatible with a difference of order $\\\\epsilon$ within the `interior\\\' of the Whitham oscillatory zone, of order $\\\\epsilon^{1/3}$ at the left boundary outside the Whitham zone and of order $\\\\epsilon^{1/2}$ at the right boundary outside the Whitham zone. %B Comm. Pure Appl. Math. 60 (2007) 1623-1664 %G en_US %U http://hdl.handle.net/1963/1788 %1 2756 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:45:26Z\\nNo. of bitstreams: 1\\n91FM-2005.pdf: 905542 bytes, checksum: 8505fe7c8ac2e5f1da7248d62ae542b2 (MD5) %R 10.1002/cpa.20183 %0 Report %D 2007 %T Numerical study of a multiscale expansion of KdV and Camassa-Holm equation %A Tamara Grava %A Christian Klein %X We study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlev\\\\\\\'e I hierarchy. It is shown that this solution gives a valid asymptotic description of the solutions close to breakup. We present a detailed analysis of the situation and compare the Korteweg-de Vries solution quantitatively with asymptotic solutions obtained via the solution of the Hopf and the Whitham equations. We give a qualitative analysis for the Camassa-Holm equation %G en_US %U http://hdl.handle.net/1963/2527 %1 1591 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-12T12:39:23Z\\nNo. of bitstreams: 1\\n0702038v1.pdf: 367188 bytes, checksum: f88c96f6ff42a7c5378de0118866d4bb (MD5) %0 Report %D 2007 %T Numerically flat Higgs vector bundles %A Ugo Bruzzo %A Beatriz Grana-Otero %X After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability. %B Commun. Contemp. Math. 9 (2007) 437-446 %G en_US %U http://hdl.handle.net/1963/1757 %1 2787 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-21T15:59:56Z\\nNo. of bitstreams: 1\\n39_2005_fm.pdf: 192887 bytes, checksum: 1d32aff78ef27b80046dfc391135d55a (MD5) %R 10.1142/S0219199707002526 %0 Report %D 2006 %T N=1 superpotentials from multi-instanton calculus %A Francesco Fucito %A Jose F. Morales %A Rubik Poghossian %A Alessandro Tanzini %X In this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement. %B JHEP01(2006)031 %G en_US %U http://hdl.handle.net/1963/1773 %1 2771 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-29T07:58:23Z\\nNo. of bitstreams: 1\\n73FM-2005.pdf: 325303 bytes, checksum: 89f205e907378d543e7a51042f437c8a (MD5) %R 10.1088/1126-6708/2006/01/031 %0 Report %D 2006 %T Normal bundles to Laufer rational curves in local Calabi-Yau threefolds %A Ugo Bruzzo %A Antonio Ricco %X We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points. %B Lett. Math. Phys. 76 (2006) 57-63 %G en_US %U http://hdl.handle.net/1963/1785 %1 2759 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:06:11Z\\nNo. of bitstreams: 1\\n88FM-2005.pdf: 106989 bytes, checksum: c39c0a1665f5c8185a573959a67e9a72 (MD5) %R 10.1007/s11005-006-0057-7 %0 Journal Article %J Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 %D 2005 %T Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy %A Ugo Boscain %A Thomas Chambrion %A Grégoire Charlot %X We apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed. %B Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 %G en_US %U http://hdl.handle.net/1963/2259 %1 1988 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T11:55:27Z\\nNo. of bitstreams: 1\\n0409022v2.pdf: 578605 bytes, checksum: db7298996e781c3a8546c3d01ee28384 (MD5) %0 Report %D 2005 %T Nonlinear Schrödinger Equations with vanishing and decaying potentials %A Antonio Ambrosetti %A Wang Zhi-Qiang %B Differential Integral Equations 18 (2005), no. 12, 1321-1332 %G en_US %U http://hdl.handle.net/1963/1760 %1 2784 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-22T09:32:48Z\\nNo. of bitstreams: 1\\n52M-2005.pdf: 2540023 bytes, checksum: a022763e63174283e8e626a5c191eb2a (MD5) %0 Journal Article %J Mod. Phys. Lett. A 18 (2003) 2371-2379 %D 2003 %T Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces %A Ludwik Dabrowski %A Thomas Krajewski %A Giovanni Landi %X We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$. %B Mod. Phys. Lett. A 18 (2003) 2371-2379 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3215 %1 1086 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T11:23:21Z\\nNo. of bitstreams: 1\\n0309143v1.pdf: 165627 bytes, checksum: c79b1a62edf34ae51819b5e8d752db8b (MD5) %R 10.1142/S0217732303012593 %0 Journal Article %J Commun. Pure Appl. Ana., 2003, 2, 51-64 %D 2003 %T A note on singular limits to hyperbolic systems of conservation laws %A Stefano Bianchini %X In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. \\nUnder the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation. %B Commun. Pure Appl. Ana., 2003, 2, 51-64 %I SISSA Library %G en %U http://hdl.handle.net/1963/1542 %1 2621 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:52Z (GMT). No. of bitstreams: 1\\nmath.AP0009012.pdf: 134454 bytes, checksum: 922fd2c2a00dd9dd36fc10453824437c (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Rend. Mat. Appl. 23 (2003) 189-201 %D 2003 %T A note on the integral representation of functionals in the space SBD(O) %A Francois Ebobisse %A Rodica Toader %X In this paper we study the integral representation in the space SBD(O) of special functions with bounded deformation of some L^1-norm lower semicontinuous functionals invariant with respect to rigid motions. %B Rend. Mat. Appl. 23 (2003) 189-201 %I Rendiconti di Matematica %G en_US %U http://hdl.handle.net/1963/3064 %1 1269 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T08:08:06Z\\nNo. of bitstreams: 1\\n0104264v1.pdf: 157593 bytes, checksum: 8afd09d4c0f34e5fa55e357804395f3d (MD5) %0 Journal Article %J J. Funct. Anal. 180 (2001) 210-241 %D 2001 %T Non-compactness and multiplicity results for the Yamabe problem on Sn %A Massimiliano Berti %A Andrea Malchiodi %B J. Funct. Anal. 180 (2001) 210-241 %I Elsevier %G en %U http://hdl.handle.net/1963/1345 %1 3110 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:35Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1006/jfan.2000.3699 %0 Journal Article %J J. Geom. Phys. 37 (2001), no. 1-2, 169-181 %D 2001 %T A note on the super Krichever map %A Gregorio Falqui %A Cesare Reina %A Alessandro Zampa %X We consider the geometrical aspects of the Krichever map in the context of Jacobian Super KP hierarchy. We use the representation of the hierarchy based\\non the Fa`a di Bruno recursion relations, considered as the cocycle condition for the natural double complex associated with the deformations of super Krichever data. Our approach is based on the construction of the universal super divisor (of degree g), and a local universal family of geometric data which give the map into the Super Grassmannian. %B J. Geom. Phys. 37 (2001), no. 1-2, 169-181 %I SISSA Library %G en %U http://hdl.handle.net/1963/1494 %1 2669 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:03:11Z (GMT). No. of bitstreams: 1\\nnlin.SI0005062.pdf: 195729 bytes, checksum: daafbab4268655b8f1445ff39762b659 (MD5)\\n Previous issue date: 2000 %R 10.1016/S0393-0440(00)00037-1 %0 Thesis %D 2001 %T Numerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence %A Matteo Negri %K Mumford-Shah functional %I SISSA %G en %U http://hdl.handle.net/1963/5399 %1 5226 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-02-08T08:42:37Z\\nNo. of bitstreams: 1\\nPhD_Negri_Matteo.pdf: 9815789 bytes, checksum: 517224e4dfc63645a4ba399a34d9cb8f (MD5) %0 Journal Article %J Calcolo, 2001, 38, 67 %D 2001 %T Numerical minimization of the Mumford-Shah functional %A Matteo Negri %A Maurizio Paolini %B Calcolo, 2001, 38, 67 %I SISSA Library %G en %U http://hdl.handle.net/1963/1461 %1 3079 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:02:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1007/s100920170004 %0 Journal Article %J Ricerche Mat. 49 (2000), suppl., 169-176 %D 2000 %T A note on the scalar curvature problem in the presence of symmetries %A Antonio Ambrosetti %A Li YanYan %A Andrea Malchiodi %B Ricerche Mat. 49 (2000), suppl., 169-176 %I SISSA Library %G en %U http://hdl.handle.net/1963/1365 %1 3090 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:52Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J J. Differential Equations 151 (1999) 345-372 %D 1999 %T Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws %A Debora Amadori %A Paolo Baiti %A Philippe G. LeFloch %A Benedetto Piccoli %X The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality. %B J. Differential Equations 151 (1999) 345-372 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3312 %1 1018 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-20T11:49:26Z\\nNo. of bitstreams: 1\\nNonclassical_shocks.pdf: 261875 bytes, checksum: bd41bb6490895996b965941b1eeb6797 (MD5) %R 10.1006/jdeq.1998.3513 %0 Journal Article %D 1999 %T A note on fractional KDV hierarchies. II. The bihamiltonian approach %A Paolo Casati %A Gregorio Falqui %A Marco Pedroni %I SISSA Library %G en %U http://hdl.handle.net/1963/1220 %1 2723 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:54:55Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J J. Math. Phys. 31 (1990), no.4, 948-952 %D 1990 %T N=2 super Riemann surfaces and algebraic geometry %A Cesare Reina %A Gregorio Falqui %X The geometric framework for N=2 superconformal field theories are described by studying susy2 curves-a nickname for N=2 super Riemann surfaces. It is proved that \\\"single\\\'\\\' susy2 curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems. %B J. Math. Phys. 31 (1990), no.4, 948-952 %I American Institute of Physics %G en %U http://hdl.handle.net/1963/807 %1 2984 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:38:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1989 %R 10.1063/1.528775 %0 Journal Article %J Comm.Math.Phys. 31 (1990), no.4, 948 %D 1990 %T A note on the global structure of supermoduli spaces %A Cesare Reina %A Gregorio Falqui %B Comm.Math.Phys. 31 (1990), no.4, 948 %I SISSA Library %G en %U http://hdl.handle.net/1963/806 %1 2985 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:38:11Z (GMT). No. of bitstreams: 1\\n46_89.pdf: 522357 bytes, checksum: 18f63d98e1ce1e711e039894ded5ae7c (MD5)\\n Previous issue date: 1989 %0 Journal Article %J Boll. Un. Mat. Ital. B (7) 3 (1989), no. 3, 579-590 %D 1989 %T On the number of families of periodic solutions of a Hamiltonian system near equilibrium. II. (English. Italian summary) %A Gianfausto Dell'Antonio %A Biancamaria D'Onofrio %B Boll. Un. Mat. Ital. B (7) 3 (1989), no. 3, 579-590 %I SISSA Library %G en %U http://hdl.handle.net/1963/609 %1 3295 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:35:24Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Lett. Math. Phys. 11 (1986), no. 2, 171-175 %D 1986 %T The natural spinor connection on $S\\\\sb 8$ is a gauge field %A Giovanni Landi %B Lett. Math. Phys. 11 (1986), no. 2, 171-175 %I SISSA Library %G en %U http://hdl.handle.net/1963/448 %1 3455 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:32:34Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985