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.

1 aTezzele, Marco1 aDemo, Nicola1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/shape-optimization-through-proper-orthogonal-decomposition-interpolation-and-dynamic00406nas a2200109 4500008004100000245005200041210004800093100002400141700002000165700002500185856008600210 2019 eng d00aThe sharp quantitative isocapacitary inequality0 asharp quantitative isocapacitary inequality1 aDe Philippis, Guido1 aMarini, Michele1 aMukoseeva, Ekaterina uhttps://www.math.sissa.it/publication/sharp-quantitative-isocapacitary-inequality00668nas a2200109 4500008004100000245006600041210005900107520027500166100002500441700002100466856007100487 2019 eng d00aOn the square distance function from a manifold with boundary0 asquare distance function from a manifold with boundary3 aWe 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.

1 aBellettini, Giovanni1 aElshorbagy, Alaa uhttp://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf01020nas a2200181 4500008004100000245008500041210006900126260000800195300002100203520034100224653004000565653003600605100002000641700001800661700002100679700002000700856011800720 2019 eng d00aStrong Novikov conjecture for low degree cohomology and exotic group C*-algebras0 aStrong Novikov conjecture for low degree cohomology and exotic g cMay aarXiv:1905.077303 aWe strengthen a result of Hanke–Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

10aMathematics - K-Theory and Homology10aMathematics - Operator Algebras1 aAntonini, Paolo1 aBuss, Alcides1 aEngel, Alexander1 aSiebenand, Timo uhttps://www.math.sissa.it/publication/strong-novikov-conjecture-low-degree-cohomology-and-exotic-group-c-algebras00433nas a2200121 4500008004100000245006100041210005800102300001400160490000700174100001800181700001900199856009300218 2018 eng d00aSecond order differentiation formula on RCD(K, N) spaces0 aSecond order differentiation formula on RCDK N spaces a377–3860 v291 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-rcdk-n-spaces00386nas a2200097 4500008004100000245006100041210005700102100001800159700001900177856009200196 2018 eng d00aSecond order differentiation formula on RCD*(K,N) spaces0 aSecond order differentiation formula on RCDKN spaces1 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-rcdkn-spaces01912nas a2200157 4500008004100000245009800041210006900139260003000208520136800238100001701606700001901623700002101642700002201663700002101685856004801706 2018 eng d00aShape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition0 aShape Optimization by means of Proper Orthogonal Decomposition a aTrieste, ItalybIOS Press3 aShape 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.1 aDemo, Nicola1 aTezzele, Marco1 aGustin, Gianluca1 aLavini, Gianpiero1 aRozza, Gianluigi uhttp://ebooks.iospress.nl/publication/4922900543nas a2200133 4500008004100000245007700041210006900118260004700187300001600234490000700250100002300257700002400280856010500304 2018 eng d00aShape transitions in a soft incompressible sphere with residual stresses0 aShape transitions in a soft incompressible sphere with residual bSAGE Publications Sage UK: London, England a1507–15240 v231 aRiccobelli, Davide1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/shape-transitions-soft-incompressible-sphere-residual-stresses01292nas a2200157 4500008004100000245006900041210006900110260002100179300001200200490000700212520078900219100002901008700002401037700002301061856005001084 2018 eng d00aSingular Hartree equation in fractional perturbed Sobolev spaces0 aSingular Hartree equation in fractional perturbed Sobolev spaces bTaylor & Francis a558-5880 v253 aWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1080/14029251.2018.150342300361nas a2200109 4500008004100000245005600041210005300097100002100150700001900171700002400190856003700214 2018 eng d00aOn some rigorous aspects of fragmented condensation0 asome rigorous aspects of fragmented condensation1 aDimonte, Daniele1 aFalconi, Marco1 aOlgiati, Alessandro uhttps://arxiv.org/abs/1809.0358600348nas a2200121 4500008004100000245004500041210004400086300001100130490000700141100001800148700002200166856003800188 2018 eng d00aSpectral triples on the Jiang-Su algebra0 aSpectral triples on the JiangSu algebra a0535070 v591 aBassi, Jacopo1 aDabrowski, Ludwik uhttps://doi.org/10.1063/1.502631101002nas a2200133 4500008004100000245006100041210006000102520056900162100002200731700002100753700001900774700002700793856004800820 2018 en d00aStochastic homogenisation of free-discontinuity problems0 aStochastic homogenisation of freediscontinuity problems3 aIn 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.1 aCagnetti, Filippo1 aDal Maso, Gianni1 aScardia, Lucia1 aZeppieri, Caterina Ida uhttp://preprints.sissa.it/handle/1963/3530901093nas a2200145 4500008004100000245009200041210006900133300001300202490000800215520058600223100002100809700002300830700002400853856007000877 2018 eng d00aSymplectic invariants for parabolic orbits and cusp singularities of integrable systems0 aSymplectic invariants for parabolic orbits and cusp singularitie a201704240 v3763 aWe discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

1 aBolsinov, Alexey1 aGuglielmi, Lorenzo1 aKudryavtseva, Elena uhttps://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.042400410nas a2200097 4500008004100000245006900041210006500110100001800175700001900193856010000212 2017 eng d00aSecond order differentiation formula on compact RCD*(K,N) spaces0 aSecond order differentiation formula on compact RCDKN spaces1 aGigli, Nicola1 aTamanini, Luca uhttps://www.math.sissa.it/publication/second-order-differentiation-formula-compact-rcdkn-spaces00941nas a2200109 4500008004100000245006900041210006800110260001000178520057200188100002000760856005100780 2017 en d00aSelf-Adjoint Extensions of Dirac Operator with Coulomb Potential0 aSelfAdjoint Extensions of Dirac Operator with Coulomb Potential bSISSA3 aIn this note we give a concise review of the present state-of-art for the problem of self-adjoint realisations for the Dirac operator with a Coulomb-like singular scalar potential V(x) = Ø(x)I4. We try to follow the historical and conceptual path that leads to the present understanding of the problem and to highlight the techniques employed and the main ideas. In the final part we outline a few major open questions that concern the topical problem of the multiplicity of self-adjoint realisations of the model, and which are worth addressing in the future.1 aGallone, Matteo uhttp://urania.sissa.it/xmlui/handle/1963/3527301120nas a2200109 4500008004100000245008000041210006900121520072300190100002000913700002900933856004800962 2017 en d00aSelf-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei0 aSelfadjoint realisations of the DiracCoulomb Hamiltonian for hea3 aWe derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the KreĬn-Višik- Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neu- mann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the exten- sion, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.1 aGallone, Matteo1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3528700688nas a2200121 4500008004100000245005300041210005200094520031100146100001600457700002100473700002400494856004800518 2017 en d00aSemistable Higgs Bundles on Calabi-Yau Manifolds0 aSemistable Higgs Bundles on CalabiYau Manifolds3 aWe 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.1 aBruzzo, Ugo1 aLanza, Valeriano1 aLo Giudice, Alessio uhttp://preprints.sissa.it/handle/1963/3529501212nas a2200145 4500008004100000022001400041245008800055210007000143260000800213300001400221490000700235520076100242100001701003856004601020 2017 eng d a1573-869800aSmall Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators0 aSmall Time Asymptotics on the Diagonal for Hörmanders Type Hypoe cJan a111–1430 v233 aWe compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.

1 aPaoli, Elisa uhttps://doi.org/10.1007/s10883-016-9321-z00623nas a2200169 4500008004100000245008300041210006900124260002500193300001400218490000800232100001600240700001600256700002300272700002300295700002400318856011100342 2017 eng d00aSolid tumors are poroelastic solids with a chemo-mechanical feedback on growth0 aSolid tumors are poroelastic solids with a chemomechanical feedb bSpringer Netherlands a107–1240 v1291 aAmbrosi, D.1 aPezzuto, S.1 aRiccobelli, Davide1 aStylianopoulos, T.1 aCiarletta, Pasquale uhttps://www.math.sissa.it/publication/solid-tumors-are-poroelastic-solids-chemo-mechanical-feedback-growth01207nas a2200133 4500008004100000245006200041210006000103260001300163490000800176520080600184100002100990700002101011856004101032 2017 eng d00aA Spectral Element Reduced Basis Method in Parametric CFD0 aSpectral Element Reduced Basis Method in Parametric CFD bSpringer0 v1263 aWe 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.

1 aHess, Martin, W.1 aRozza, Gianluigi uhttps://www.math.sissa.it/node/1294600400nas a2200097 4500008004100000245006400041210006000105100002100165700002100186856009500207 2017 eng d00aA Spectral Element Reduced Basis Method in Parametric {CFD}0 aSpectral Element Reduced Basis Method in Parametric CFD1 aHess, Martin, W.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/spectral-element-reduced-basis-method-parametric-cfd01253nas a2200133 4500008004100000245007800041210006900119260001000188520080500198100001801003700002901021700002101050856004801071 2017 en d00aSpectral Properties of the 2+1 Fermionic Trimer with Contact Interactions0 aSpectral Properties of the 21 Fermionic Trimer with Contact Inte bSISSA3 aWe 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.1 aBecker, Simon1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://preprints.sissa.it/handle/1963/3530301538nas a2200157 4500008004100000022001400041245009300055210006900148260000800217300001400225490000700239520104800246100001801294700002201312856004601334 2017 eng d a1572-964800aStasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler0 aStasis domains and slip surfaces in the locomotion of a bioinspi cFeb a587–6010 v523 aWe 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.

1 aGidoni, Paolo1 aDeSimone, Antonio uhttps://doi.org/10.1007/s11012-016-0408-000453nas a2200133 4500008004100000245009600041210006900137260000700206300001100213100001900224700002100243700001800264856003700282 2017 eng d00aSymplectic geometry of the moduli space of projective structures in homological coordinates0 aSymplectic geometry of the moduli space of projective structures c06 a1–561 aBertola, Marco1 aKorotkin, Dmitry1 aNorton, Chaya uhttps://arxiv.org/abs/1506.0791800431nas a2200133 4500008004100000245004100041210004000082260001000122100002700132700001700159700002200176700002000198856007900218 2016 en d00aSecond-order structured deformations0 aSecondorder structured deformations bSISSA1 aBarroso, Ana, Cristina1 aMatias, Jose1 aMorandotti, Marco1 aOwen, David, R. uhttps://www.math.sissa.it/publication/second-order-structured-deformations00651nas a2200157 4500008004100000245009600041210006900137260005800206300001400264490000600278100001700284700001700301700002200318700002400340856012900364 2016 eng d00aShip Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model0 aShip Sinkage and Trim Predictions Based on a CAD Interfaced Full bInternational Society of Offshore and Polar Engineers a511–5180 v31 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/ship-sinkage-and-trim-predictions-based-cad-interfaced-fully-nonlinear-potential-model00397nas a2200121 4500008004100000245004500041210004500086490000900131100001900140700002000159700001300179856008300192 2016 eng d00aSimple Lie Algebras and Topological ODEs0 aSimple Lie Algebras and Topological ODEs0 v20161 aBertola, Marco1 aDubrovin, Boris1 aYang, Di uhttps://www.math.sissa.it/publication/simple-lie-algebras-and-topological-odes00434nas a2200109 4500008004100000245006500041210006200106100001900168700002500187700002200212856009000234 2016 eng d00aOn Sobolev instability of the interior problem of tomography0 aSobolev instability of the interior problem of tomography1 aBertola, Marco1 aKatsevich, Alexander1 aTovbis, Alexander uhttps://www.math.sissa.it/publication/sobolev-instability-interior-problem-tomography00428nas a2200097 4500008004100000245008000041210006900121260001000190100001900200856011100219 2016 en d00aSome results on quasistatic evolution problems for unidirectional processes0 aSome results on quasistatic evolution problems for unidirectiona bSISSA1 aCrismale, Vito uhttps://www.math.sissa.it/publication/some-results-quasistatic-evolution-problems-unidirectional-processes01439nas a2200121 4500008004100000245010500041210006900146260001000215520093000225653002301155100001801178856012101196 2016 en d00aSome results on the mathematical analysis of crack problems with forces applied on the fracture lips0 aSome results on the mathematical analysis of crack problems with bSISSA3 aThis thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u.10aFracture mechanics1 aAlmi, Stefano uhttps://www.math.sissa.it/publication/some-results-mathematical-analysis-crack-problems-forces-applied-fracture-lips01230nas a2200157 4500008004100000245009000041210006900131260002100200300001000221490000700231520073600238100001700974700001800991700001301009856005001022 2016 eng d00aSpectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds0 aSpectral analysis and the AharonovBohm effect on certain almostR bTaylor & Francis a32-500 v413 aWe study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

1 aBoscain, Ugo1 aPrandi, Dario1 aSeri, M. uhttps://doi.org/10.1080/03605302.2015.109576601093nas a2200121 4500008004100000245010400041210006900145260001000214520065500224100002300879700001800902856005100920 2016 en d00aOn the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension0 astructure of Linftyentropy solutions to scalar conservation laws bSISSA3 aWe prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

1 aBianchini, Stefano1 aMarconi, Elio uhttp://urania.sissa.it/xmlui/handle/1963/3520901192nas a2200181 4500008004100000022001400041245008800055210006900143260000800212300000700220490000900227520063800236100002200874700002000896700002600916700002400942856004400966 2016 eng d a1029-847900aSymmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index0 aSymmetry enhancements via 5d instantons qWalgebrae and 10 superc cSep a530 v20163 aWe 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.

1 aBenvenuti, Sergio1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttps://doi.org/10.1007/JHEP09(2016)05300553nas a2200145 4500008004100000245008000041210006900121260002200190300001600212490000700228100002000235700002200255700001800277856011200295 2016 eng d00aSymmetry properties of some solutions to some semilinear elliptic equations0 aSymmetry properties of some solutions to some semilinear ellipti bClasse di Scienze a1209–12340 v161 aFarina, Alberto1 aMalchiodi, Andrea1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/symmetry-properties-some-solutions-some-semilinear-elliptic-equations01018nas a2200121 4500008004100000245007900041210007000120260001000190520058700200100002900787700002900816856005100845 2015 en d00aSchödinger operators on half-line with shrinking potentials at the origin0 aSchödinger operators on halfline with shrinking potentials at th bSISSA3 aWe discuss the general model of a Schrödinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential.1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3443901475nas a2200121 4500008004100000245011300041210006900154520101400223100001801237700002501255700002201280856005101302 2015 en d00aSemicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity0 aSemicartesian surfaces and the relaxed area of maps from the pla3 aWe 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.

1 aTealdi, Lucia1 aBellettini, Giovanni1 aPaolini, Maurizio uhttp://urania.sissa.it/xmlui/handle/1963/3448301019nas a2200121 4500008004100000245008500041210006900126260001000195520053500205653002000740100002200760856011500782 2015 en d00aSharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.0 aSharp Inequalities and Blowup Analysis for Singular MoserTruding bSISSA3 aWe 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.10aMoser-Trudinger1 aMancini, Gabriele uhttps://www.math.sissa.it/publication/sharp-inequalities-and-blow-analysis-singular-moser-trudinger-embeddings00685nas a2200097 4500008004100000245008200041210006900123520032200192100002200514856005100536 2015 en d00aSingular Liouville Equations on S^2: Sharp Inequalities and Existence Results0 aSingular Liouville Equations on S2 Sharp Inequalities and Existe3 aWe 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.

1 aMancini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3448900981nas a2200121 4500008004100000245008300041210006900124260001000193520048800203653003100691100001900722856011800741 2015 en d00aSome results on anisotropic mean curvature and other phase-transition problems0 aSome results on anisotropic mean curvature and other phasetransi bSISSA3 aThe present thesis is divided into three parts. In the first part, we analyze a suitable regularization — which we call nonlinear multidomain model — of the motion of a hypersurface under smooth anisotropic mean curvature flow. The second part of the thesis deals with crystalline mean curvature of facets of a solid set of R^3 . Finally, in the third part we study a phase-transition model for Plateau’s type problems based on the theory of coverings and of BV functions.10aAnisotropic mean curvature1 aAmato, Stefano uhttps://www.math.sissa.it/publication/some-results-anisotropic-mean-curvature-and-other-phase-transition-problems01282nas a2200121 4500008004100000245007500041210006900116260001000185520086400195100002901059700002101088856005101109 2015 en d00aStability of closed gaps for the alternating Kronig-Penney Hamiltonian0 aStability of closed gaps for the alternating KronigPenney Hamilt bSISSA3 aWe 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.1 aMichelangeli, Alessandro1 aMonaco, Domenico uhttp://urania.sissa.it/xmlui/handle/1963/3446001228nas a2200109 4500008004100000245007200041210006700113520083900180100002901019700001901048856005101067 2015 en d00aStability of the (2+2)-fermionic system with zero-range interaction0 aStability of the 22fermionic system with zerorange interaction3 aWe 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.1 aMichelangeli, Alessandro1 aPfeiffer, Paul uhttp://urania.sissa.it/xmlui/handle/1963/3447402147nas a2200157 4500008004100000245008700041210006900128260001000197300001200207490000700219520161800226653002801844100002001872700002501892856007201917 2015 en d00aStable regular critical points of the Mumford-Shah functional are local minimizers0 aStable regular critical points of the MumfordShah functional are bSISSA a533-5700 v323 aIn this paper it is shown that any regular critical point of the Mumford–Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$

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

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

1 aCicconofri, Giancarlo1 aDeSimone, Antonio uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.005400689nas a2200145 4500008004100000245009900041210006900140260001000209520018600219100002400405700002000429700002200449700002100471856005100492 2015 en d00aSupremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations0 aSupremizer stabilization of PODGalerkin approximation of paramet bWiley3 aIn this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number.1 aBallarin, Francesco1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3470101557nas a2200121 4500008004100000245012000041210006900161260001300230520109900243100002101342700002101363856005101384 2015 en d00aSymmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry0 aSymmetry and localization in periodic crystals triviality of Blo bSpringer3 aWe describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, called the Bloch bundle. The rôle of additional Z_2-symmetries, as time-reversal and space-reflection symmetry, is discussed, showing how time-reversal symmetry implies the triviality of the Bloch bundle, both in the bosonic and in the fermionic case. Moreover, the same Z_2-symmetry allows to define a finer notion of isomorphism and, consequently, to define new topological invariants, which agree with the indices introduced by Fu, Kane and Mele in the context of topological insulators.

1 aMonaco, Domenico1 aPanati, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3446800632nas a2200109 4500008004100000245008300041210007100124260001300195520024000208100002300448856005100471 2014 en d00aSBV Regularity of Systems of Conservation Laws and Hamilton–Jacobi Equations0 aSBV Regularity of Systems of Conservation Laws and Hamilton–Jaco bSpringer3 aWe 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.1 aBianchini, Stefano uhttp://urania.sissa.it/xmlui/handle/1963/3469101169nas a2200145 4500008004100000245008500041210006900126260001000195520065500205653006700860100002100927700001900948700002000967856003600987 2014 en d00aSecond Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional0 aSecond Order Asymptotic Development for the Anisotropic CahnHill bSISSA3 aThe 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.10aGamma-convergence, Cahn-Hilliard functional, phase transitions1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/739001605nas a2200121 4500008004100000245008400041210006900125260002200194520117200216100002001388700002401408856005101432 2014 en d00aSemiclassical limit of focusing NLS for a family of square barrier initial data0 aSemiclassical limit of focusing NLS for a family of square barri bWiley Periodicals3 aThe small dispersion limit of the focusing nonlinear Schrödinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data,the family of square barriers,ψ 0(x) = qχ[-L,L] for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O(1) maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data.1 aJenkins, Robert1 aMcLaughlin, Kenneth uhttp://urania.sissa.it/xmlui/handle/1963/3506601649nas a2200121 4500008004100000245007500041210006900116260001300185520123700198100001901435700002201454856005101476 2014 en d00aShape control of active surfaces inspired by the movement of euglenids0 aShape control of active surfaces inspired by the movement of eug bElsevier3 aWe 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.1 aArroyo, Marino1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3511801626nas a2200145 4500008004100000245010700041210006900148260001300217520111600230100002401346700002001370700002101390700001801411856005101429 2014 en d00aShape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows0 aShape Optimization by FreeForm Deformation Existence Results and bSpringer3 aShape 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.1 aBallarin, Francesco1 aManzoni, Andrea1 aRozza, Gianluigi1 aSalsa, Sandro uhttp://urania.sissa.it/xmlui/handle/1963/3469800581nas a2200109 4500008004100000245016900041210006900210100001900279700002500298700002200323856012600345 2014 eng d00aSingular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach0 aSingular Value Decomposition of a Finite Hilbert Transform Defin1 aBertola, Marco1 aKatsevich, Alexander1 aTovbis, Alexander uhttps://www.math.sissa.it/publication/singular-value-decomposition-finite-hilbert-transform-defined-several-intervals-and01519nas a2200145 4500008004100000245015300041210006900194260001300263520096300276100002001239700002301259700002401282700001601306856005101322 2014 en d00aSix-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics0 aSixdimensional supersymmetric gauge theories quantum cohomology bSpringer3 aWe 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.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr uhttp://urania.sissa.it/xmlui/handle/1963/3454600707nas a2200145 4500008004100000022001400041245007900055210006900134300001400203490000700217520023000224100001700454700001900471856007100490 2014 eng d a0294-144900aSmooth approximation of bi-Lipschitz orientation-preserving homeomorphisms0 aSmooth approximation of biLipschitz orientationpreserving homeom a567 - 5890 v313 aWe 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.

1 aDaneri, Sara1 aPratelli, Aldo uhttp://www.sciencedirect.com/science/article/pii/S029414491300071100987nas a2200145 4500008004100000245008700041210006900128260001000197520050200207100002400709700002000733700001900753700001900772856005000791 2014 en d00aSome remarks on a model for rate-independent damage in thermo-visco-elastodynamics0 aSome remarks on a model for rateindependent damage in thermovisc bSISSA3 aThis 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.1 aLazzaroni, Giuliano1 aRossi, Riccarda1 aThomas, Marita1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/746301769nas a2200133 4500008004100000245008300041210006900124260001900193520130400212100002001516700002101536700002701557856005101584 2014 en d00aSome remarks on the seismic behaviour of embedded cantilevered retaining walls0 aSome remarks on the seismic behaviour of embedded cantilevered r bThomas Telford3 aThis 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.1 aConti, Riccardo1 aD'Arezzo, Burali1 aViggiani, Giulia, M.B. uhttp://urania.sissa.it/xmlui/handle/1963/3507300993nas a2200121 4500008004100000245006500041210006500106260003000171520058100201100001600782700002200798856005100820 2014 en d00aSpontaneous division and motility in active nematic droplets0 aSpontaneous division and motility in active nematic droplets bAmerican Physical Society3 aWe 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.1 aGiomi, Luca1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3490200979nas a2200157 4500008004100000022004000041245009000081210006900171260001900240300001200259490000600271520039700277653003900674100002000713856008800733 2014 en d aOnline: 1864-8266; Print: 1864-825800aStability of equilibrium configurations for elastic films in two and three dimensions0 aStability of equilibrium configurations for elastic films in two bSISSAc01/2014 a117-1530 v83 aWe 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.

10aEpitaxially strained elastic films1 aBonacini, Marco uhttps://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml01201nas a2200133 4500008004100000245007800041210006900119300001100188490000800199520070800207100001900915700002100934856011200955 2014 eng d00aStabilized reduced basis method for parametrized advection-diffusion PDEs0 aStabilized reduced basis method for parametrized advectiondiffus a1–180 v2743 aIn this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We explain why the stabilization is needed in both stages and we identify, analytically and numerically, which are the drawbacks of a stabilization performed only during the construction of the reduced basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances of the ``double'' stabilization both in steady and unsteady problems, also related to heat transfer phenomena.

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/stabilized-reduced-basis-method-parametrized-advection-diffusion-pdes01104nas a2200121 4500008004100000245016100041210006900202300001600271520058500287100001900872700002100891856007000912 2014 eng d00aStabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts0 aStabilized reduced basis method for parametrized scalar advectio a5614–56243 aAdvection-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.

1 aPacciarini, P.1 aRozza, Gianluigi uhttps://infoscience.epfl.ch/record/203327/files/ECCOMAS_PP_GR.pdf00470nas a2200109 4500008004100000245008400041210006900125260001000194100002300204700001600227856011700243 2014 en d00aSteady nearly incompressible vector elds in 2D: chain rule and renormalization0 aSteady nearly incompressible vector elds in 2D chain rule and re bSISSA1 aBianchini, Stefano1 aGusev, N.A. uhttps://www.math.sissa.it/publication/steady-nearly-incompressible-vector-elds-2d-chain-rule-and-renormalization01412nas a2200145 4500008004100000245004500041210004100086260001300127520099200140100002001132700002301152700002401175700001601199856005101215 2014 en d00aThe stringy instanton partition function0 astringy instanton partition function bSpringer3 aWe 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^2.1 aBonelli, Giulio1 aSciarappa, Antonio1 aTanzini, Alessandro1 aVasko, Petr uhttp://urania.sissa.it/xmlui/handle/1963/3458901002nas a2200133 4500008004100000245005800041210005500099260001000154520060700164100002100771700002000792700002000812856003600832 2014 en d00aStructure of classical (finite and affine) W-algebras0 aStructure of classical finite and affine Walgebras bSISSA3 aFirst, 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.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/731400484nas a2200133 4500008004100000245009400041210006900135260001900204300001200223490000800235100002300243700001200266856007200278 2014 en d00aStructure of entropy solutions to general scalar conservation laws in one space dimension0 aStructure of entropy solutions to general scalar conservation la bSISSAc08/2015 a356-3860 v4281 aBianchini, Stefano1 aYu, Lei uhttps://www.sciencedirect.com/science/article/pii/S0022247X1500221801169nas a2200133 4500008004100000245007700041210006900118260003400187520069100221100002700912700002300939700002200962856005100984 2014 en d00aSwelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch0 aSwelling dynamics of a thin elastomeric sheet under uniaxial pre bAmerican Institute of Physics3 aIt 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.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3511301394nas a2200133 4500008004100000245006500041210006400106260002800170520094000198100002701138700002301165700002101188856005101209 2014 en d00aSwelling-induced and controlled curving in layered gel beams0 aSwellinginduced and controlled curving in layered gel beams bRoyal Society of London3 aWe 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.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aPezzulla, Matteo uhttp://urania.sissa.it/xmlui/handle/1963/3498700494nas a2200097 4500008004100000245012100041210006900162100001700231700001800248856013000266 2013 eng d00aSelf-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces0 aSelfadjoint extensions and stochastic completeness of the Laplac1 aBoscain, Ugo1 aPrandi, Dario uhttps://www.math.sissa.it/publication/self-adjoint-extensions-and-stochastic-completeness-laplace-beltrami-operator-conic-and00943nas a2200121 4500008004100000245004000041210004000081260001000121520053200131653010100663100002100764856003600785 2013 en d00aSemistability and Decorated Bundles0 aSemistability and Decorated Bundles bSISSA3 aThis thesis is devoted to the study of semistability condition of type t=(a,b,c,N) decorated bundles and sheaves in order to better understand and simplify it. We approach the problem in two different ways: on one side we “enclose” the above semistability condition between a stronger semistability condition (\epsilon-semistability) and a weaker one (k-semistability), on the other side we try, and succeed for the case of a = 2, to bound the length of weighted filtrations on which one checks the semistability condition.10aDecorated sheaves, semistability, moduli space, Mehta-Ramanathan, maximal destabilizing subsheaf1 aPustetto, Andrea uhttp://hdl.handle.net/1963/713001064nas a2200109 4500008004100000245002900041210002900070260001000099520079300109100001600902856003600918 2013 en d00aSoftly Constrained Films0 aSoftly Constrained Films bSISSA3 aThe 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.1 aGiomi, Luca uhttp://hdl.handle.net/1963/656300403nas a2200109 4500008004100000245005300041210005300094260001000147653003300157100001800190856008500208 2013 en d00aSome models of crack growth in brittle materials0 aSome models of crack growth in brittle materials bSISSA10aQuasi-static crack evolution1 aRacca, Simone uhttps://www.math.sissa.it/publication/some-models-crack-growth-brittle-materials00401nas a2200121 4500008004100000245002300041210002300064260001000087520010800097653001300205100002500218856003600243 2013 en d00aSome open problems0 aSome open problems bSISSA3 aWe discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.10aGeometry1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/707000835nas a2200145 4500008004100000245006200041210006200103260001000165490000600175520040600181653002300587100002400610700001900634856003600653 2013 en d00aSome remarks on the viscous approximation of crack growth0 aSome remarks on the viscous approximation of crack growth bSISSA0 v63 aWe 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.

10aVariational models1 aLazzaroni, Giuliano1 aToader, Rodica uhttp://hdl.handle.net/1963/420601894nas a2200121 4500008004100000245008300041210006900124260001000193520137300203653005401576100002401630856011801654 2013 en d00aSome topics on Higgs bundles over projective varieties and their moduli spaces0 aSome topics on Higgs bundles over projective varieties and their bSISSA3 aIn 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.10aAlgebraic Geometry, Moduli spaces, Vector bundles1 aLo Giudice, Alessio uhttps://www.math.sissa.it/publication/some-topics-higgs-bundles-over-projective-varieties-and-their-moduli-spaces00539nas a2200157 4500008004100000022001400041245011800055210006900173300001400242490000800256100001900264700001900283700001600302700001500318856004800333 2013 eng d a0022-471500aSpectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes0 aSpectra of random Hermitian matrices with a smallrank external s a654–6970 v1531 aBertola, Marco1 aBuckingham, R.1 aLee, S., Y.1 aPierce, V. uhttp://dx.doi.org/10.1007/s10955-013-0845-200744nas a2200097 4500008004100000245004800041210004300089520044800132100001800580856004800598 2013 en d00aThe splitting theorem in non-smooth context0 asplitting theorem in nonsmooth context3 aWe prove that an infinitesimally Hilbertian $CD(0,N)$ space containing a line splits as the product of $R$ and an infinitesimally Hilbertian $CD(0,N −1)$ space. By ‘infinitesimally Hilbertian’ we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.1 aGigli, Nicola uhttp://preprints.sissa.it/handle/1963/3530601218nas a2200121 4500008004100000245008200041210006900123520080800192100002201000700002301022700001501045856003601060 2013 en d00aStabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control0 aStabilization of Stochastic Quantum Dynamics via Open and Closed3 aIn 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 control1 aAltafini, Claudio1 aTicozzi, Francesco1 aNishio, K. uhttp://hdl.handle.net/1963/650301660nas a2200145 4500008004100000245010800041210006900149260001000218520115900228653003501387100001701422700001701439700002201456856003601478 2013 en d00aA stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions0 astable and adaptive semiLagrangian potential model for unsteady bSISSA3 aWe 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.

10aUnsteady ship-wave interaction1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/566900757nas a2200133 4500008004100000245008600041210006900127260002100196300001200217490000700229520031600236100002200552856004900574 2013 eng d00aStable determination of a body immersed in a fluid: the nonlinear stationary case0 aStable determination of a body immersed in a fluid the nonlinear bTaylor & Francis a460-4810 v923 aWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier–Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log–log type.

1 aBallerini, Andrea uhttps://doi.org/10.1080/00036811.2011.62817301509nas a2200145 4500008004100000245009700041210006900138300001600207490000700223520095300230100001501183700002201198700002101220856012201241 2013 eng d00aStochastic optimal robin boundary control problems of advection-dominated elliptic equations0 aStochastic optimal robin boundary control problems of advectiond a2700–27220 v513 aIn 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.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/stochastic-optimal-robin-boundary-control-problems-advection-dominated-elliptic00584nas a2200145 4500008004100000022001400041245010700055210006900162300001500231490000700246100001900253700001700272700002000289856012900309 2013 eng d a0022-248800aStrong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model0 aStrong asymptotics for Cauchy biorthogonal polynomials with appl a043517, 250 v541 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttps://www.math.sissa.it/publication/strong-asymptotics-cauchy-biorthogonal-polynomials-application-cauchy-two-matrix-model00932nas a2200109 4500008004100000245011500041210006900156260001000225520044500235100001200680856013000692 2013 en d00aThe structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension0 astructure and regularity of admissible BV solutions to hyperboli bSISSA3 aThis thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws.1 aYu, Lei uhttps://www.math.sissa.it/publication/structure-and-regularity-admissible-bv-solutions-hyperbolic-conservation-laws-one-space01092nas a2200205 4500008004100000022001400041245010400055210006900159300000700228490000700235520037600242653003000618653003400648653002300682653003700705653002600742100002300768700001900791856007600810 2013 eng d a1078-094700aSubharmonic solutions for nonlinear second order equations in presence of lower and upper solutions0 aSubharmonic solutions for nonlinear second order equations in pr a890 v333 aWe 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.

10alower and upper solutions10aparameter dependent equations10aPeriodic solutions10aPoincaré-Birkhoff twist theorem10asubharmonic solutions1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f00380nas a2200109 4500008004100000245007400041210006900115260001000184100002300194700001700217856003600234 2013 en d00aOn Sudakov's type decomposition of transference plans with norm costs0 aSudakovs type decomposition of transference plans with norm cost bSISSA1 aBianchini, Stefano1 aDaneri, Sara uhttp://hdl.handle.net/1963/720600812nas a2200133 4500008004100000245006300041210006200104260003000166520036300196100001600559700002600575700002600601856005100627 2013 en d00aSymplectic instanton bundles on P3 and 't Hooft instantons0 aSymplectic instanton bundles on P3 and t Hooft instantons barXiv:1312.5554 [math.AG]3 aWe introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of 't Hooft instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3448600431nas a2200109 4500008004300000245011600043210006900159260001300228100002300241700002100264856003600285 2012 en_Ud 00aSBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension0 aSBV regularity for genuinely nonlinear strictly hyperbolic syste bSpringer1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/409100447nas a2200133 4500008004100000245008500041210006900126260001000195300001400205490000700219100002300226700001900249856004500268 2012 en d00aSBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)0 aSBV regularity for HamiltonJacobi equations with Hamiltonian dep bSISSA a2179-22030 v441 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1406600755nas a2200121 4500008004100000245010500041210006900146260001300215520032300228653002300551100002300574856003600597 2012 en d00aSBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension0 aSBV regularity of genuinely nonlinear hyperbolic systems of cons bElsevier3 aThe 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; regularity10aHyperbolic systems1 aBianchini, Stefano uhttp://hdl.handle.net/1963/653500509nas a2200121 4500008004100000245009900041210006900140300001400209490000700223100002300230700001200253856012200265 2012 eng d00aSBV-like regularity for general hyperbolic systems of conservation laws in one space dimension0 aSBVlike regularity for general hyperbolic systems of conservatio a439–4720 v441 aBianchini, Stefano1 aYu, Lei uhttps://www.math.sissa.it/publication/sbv-regularity-general-hyperbolic-systems-conservation-laws-one-space-dimension00441nas a2200133 4500008004100000245008000041210006900121260001000190300001200200490000800212100002300220700001900243856004500262 2012 en d00aSBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian0 aSBVlike regularity for HamiltonJacobi equations with a convex Ha bSISSA a190-2080 v3911 aBianchini, Stefano1 aTonon, Daniela uhttp://hdl.handle.net/20.500.11767/1390901260nas a2200193 4500008004100000022001400041245008600055210006900141300000900210490000700219520060600226653002800832653002500860653002800885653002700913653002400940100002600964856007600990 2012 eng d a1078-094700aSecond order approximations of quasistatic evolution problems in finite dimension0 aSecond order approximations of quasistatic evolution problems in a11250 v323 aIn 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.

10adiscrete approximations10aperturbation methods10asaddle-node bifurcation10aSingular perturbations10avanishing viscosity1 aAgostiniani, Virginia uhttp://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f801314nas a2200133 4500008004100000245005400041210005200095260002100147300001100168490000600179520092400185100002201109856004901131 2012 eng d00aSelf-propelled micro-swimmers in a Brinkman fluid0 aSelfpropelled microswimmers in a Brinkman fluid bTaylor & Francis a88-1030 v63 aWe 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.

1 aMorandotti, Marco uhttps://doi.org/10.1080/17513758.2011.61126001580nas a2200145 4500008004100000245008700041210006900128260001000197520093400207653011301141100001501254700002201269700002101291856012201312 2012 en d00aSimulation-based uncertainty quantification of human arterial network hemodynamics0 aSimulationbased uncertainty quantification of human arterial net bWiley3 aThis 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.10auncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/simulation-based-uncertainty-quantification-human-arterial-network-hemodynamics01296nas a2200145 4500008004100000022001300041245010400054210006900158300001400227490000700241520073600248100002400984700002001008856012201028 2012 eng d a0951771500aSobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential0 aSobolev quasiperiodic solutions of multidimensional wave equatio a2579-26130 v253 aWe prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d ≥ 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11]. © 2012 IOP Publishing Ltd.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/sobolev-quasi-periodic-solutions-multidimensional-wave-equations-multiplicative01270nas a2200109 4500008004100000245012700041210007000168260002800238520083700266100002101103856003601124 2012 en d00aSolving the Sixth Painlevé Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae0 aSolving the Sixth Painlevé Equation Towards the Classification o bOxford University Press3 aThe 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.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/609300790nas a2200121 4500008004100000245014600041210006900187300001400256490000600270520032300276100001900599856005000618 2012 eng d00aSome applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to ConvectionTheory and sticky particles0 aSome applications of the SBV Regularity Theorem for entropy solu a163–1750 v33 aWe 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.

1 aTonon, Daniela uhttps://hal.archives-ouvertes.fr/hal-0091840900324nas a2200097 4500008004100000245006100041210005700102260001000159100002100169856003600190 2012 en d00aSome aspects of spinors – classical and noncommutative0 aSome aspects of spinors classical and noncommutative bSISSA1 aDossena, Giacomo uhttp://hdl.handle.net/1963/631700568nas a2200121 4500008004100000245003800041210003800079260003200117520021000149653002200359100002900381856003600410 2012 en d00aSome remarks on quantum mechanics0 aSome remarks on quantum mechanics bWorld Scientific Publishing3 aWe 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.10aQuantum mechanics1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/701800559nas a2200157 4500008004100000022001400041245011500055210006900170300001400239490000800253100001900261700001900280700001600299700001500315856007100330 2012 eng d a0022-471500aSpectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes0 aSpectra of random Hermitian matrices with a smallrank external s a475–5180 v1461 aBertola, Marco1 aBuckingham, R.1 aLee, S., Y.1 aPierce, V. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-201607nas a2200157 4500008004100000245009600041210006900137260002100206520106500227100002201292700002901314700002001343700002901363700002101392856003601413 2012 en d00aStability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions0 aStability for a System of N Fermions Plus a Different Particle w bWorld Scientific3 aWe 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.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://hdl.handle.net/1963/606900518nas a2200109 4500008004100000245011900041210006900160100001700229700001700246700002200263856012300285 2012 eng d00aA stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves0 astable semilagrangian potential method for the simulation of shi1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/stable-semi-lagrangian-potential-method-simulation-ship-interaction-unsteady-and00752nas a2200121 4500008004100000245004700041210004600088260001000134520040400144100002500548700002100573856003600594 2012 en d00aSub-Riemannian structures on 3D Lie groups0 aSubRiemannian structures on 3D Lie groups bSISSA3 aWe 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.

1 aAgrachev, Andrei, A.1 aBarilari, Davide uhttp://hdl.handle.net/1963/645300723nas a2200121 4500008004100000245003800041210003800079260001000117520039200127100002500519700002100544856003600565 2012 en d00aSystems of Quadratic Inequalities0 aSystems of Quadratic Inequalities bSISSA3 aWe 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_2.1 aAgrachev, Andrei, A.1 aLerario, Antonio uhttp://hdl.handle.net/1963/707200804nas a2200133 4500008004100000245005600041210005400097260001300151520040700164100002300571700002300594700001700617856003600634 2011 en d00aSBV regularity for Hamilton-Jacobi equations in R^n0 aSBV regularity for HamiltonJacobi equations in Rn bSpringer3 aIn 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 $SBV_{loc}(\Omega)$.

1 aBianchini, Stefano1 aDe Lellis, Camillo1 aRobyr, Roger uhttp://hdl.handle.net/1963/491101465nas a2200121 4500008004300000245006700043210006500110260001300175520107800188100001601266700002501282856003601307 2011 en_Ud 00aSemistable and numerically effective principal (Higgs) bundles0 aSemistable and numerically effective principal Higgs bundles bElsevier3 aWe study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian–Yang–Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/363801135nas a2200145 4500008004300000245008100043210006900124260002300193520065600216100002100872700002100893700001900914700002000933856003600953 2011 en_Ud 00aSingular perturbation models in phase transitions for second order materials0 aSingular perturbation models in phase transitions for second ord bIndiana University3 aA 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.1 aChermisi, Milena1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/385801019nas a2200133 4500008004100000020001800041245004500059210004500104260001000149520064400159653002500803100002100828856003600849 2011 en d a978311027558200aSolving PVI by Isomonodromy Deformations0 aSolving PVI by Isomonodromy Deformations bSISSA3 aThe 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, 2011.10aPainlevé Equations1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652200674nas a2200121 4500008004100000245006800041210006100109260001000170520028700180653002400467100002500491856003600516 2011 en d00aOn the Space of Symmetric Operators with Multiple Ground States0 aSpace of Symmetric Operators with Multiple Ground States bSISSA3 aWe 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.10aMultiple eigenvalue1 aAgrachev, Andrei, A. uhttp://hdl.handle.net/1963/706900991nas a2200169 4500008004100000245009900041210006900140260001300209300001200222490000800234520046000242100002100702700002300723700002000746700001900766856003600785 2011 en d00aThe sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry0 asphere and the cut locus at a tangency point in twodimensional a bSpringer a141-1610 v17 3 aWe 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.

1 aBonnard, Bernard1 aCharlot, Grégoire1 aGhezzi, Roberta1 aJanin, Gabriel uhttp://hdl.handle.net/1963/491400415nas a2200121 4500008004100000245007100041210006900112260001000181100002200191700002300213700002100236856003600257 2011 en d00aStructure of level sets and Sard-type properties of Lipschitz maps0 aStructure of level sets and Sardtype properties of Lipschitz map bSISSA1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://hdl.handle.net/1963/465700512nas a2200121 4500008004100000245008400041210006900125260003700194300001300231490000700244100002300251856011600274 2011 eng d00aSubharmonic solutions of planar Hamiltonian systems: a rotation number approach0 aSubharmonic solutions of planar Hamiltonian systems a rotation n bAdvanced Nonlinear Studies, Inc. a77–1030 v111 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/subharmonic-solutions-planar-hamiltonian-systems-rotation-number-approach00785nas a2200121 4500008004100000245009300041210006900134300001400203490000700217520028800224100002300512856012800535 2011 eng d00aSubharmonic solutions of planar Hamiltonian systems via the Poincaré́-Birkhoff theorem0 aSubharmonic solutions of planar Hamiltonian systems via the Poin a115–1220 v663 aWe 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.

1 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/subharmonic-solutions-planar-hamiltonian-systems-poincar%C3%A9%CC%81-birkhoff-theorem00731nas a2200133 4500008004300000245007500043210006900118260002800187520027600215100002200491700002600513700002200539856003600561 2011 en_Ud 00aSupercritical conformal metrics on surfaces with conical singularities0 aSupercritical conformal metrics on surfaces with conical singula bOxford University Press3 aWe 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.

1 aBardelloni, Mauro1 aDe Marchis, Francesca1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/409501822nas a2200145 4500008004100000245009200041210006900133260002800202520132600230100002101556700002201577700001901599700002201618856003601640 2011 en d00aA system-level approach for deciphering the transcriptional response to prion infection0 asystemlevel approach for deciphering the transcriptional respons bOxford University Press3 aMOTIVATION: 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.1 aZampieri, Mattia1 aLegname, Giuseppe1 aSegrè, Daniel1 aAltafini, Claudio uhttp://hdl.handle.net/1963/574500486nas a2200121 4500008004100000245011700041210006900158260003300227300001400260490000700274100002700281856005600308 2010 eng d00aSemiclassical evolution of two rotating solitons for the Nonlinear Schrödinger Equation with electric potential0 aSemiclassical evolution of two rotating solitons for the Nonline bKhayyam Publishing, Inc.c03 a315–3480 v151 aSelvitella, Alessandro uhttps://projecteuclid.org:443/euclid.ade/135585475201102nas a2200109 4500008004300000245007400043210006900117520073300186100002100919700001600940856003600956 2010 en_Ud 00aOn semistable principal bundles over complex projective manifolds, II0 asemistable principal bundles over complex projective manifolds I3 aLet (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.1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/340400622nas a2200109 4500008004300000245010100043210006900144520021400213100002900427700002000456856003600476 2010 en_Ud 00aSharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials0 aSharp nonexistence results for a linear elliptic inequality invo3 aIn 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.1 aFall, Mouhamed Moustapha1 aMusina, Roberta uhttp://hdl.handle.net/1963/386900794nas a2200121 4500008004300000245008000043210006900123520037400192100001900566700002500585700002600610856003600636 2010 en_Ud 00aShell theories arising as low energy Gamma-limit of 3d nonlinear elasticity0 aShell theories arising as low energy Gammalimit of 3d nonlinear 3 aWe 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.1 aLewicka, Marta1 aMora, Maria Giovanna1 aPakzad, Mohammad Reza uhttp://hdl.handle.net/1963/260101245nas a2200145 4500008004100000022001300041245008800054210006900142300001200211490000800223520070400231100002400935700002000959856012000979 2010 eng d a0003952700aSobolev periodic solutions of nonlinear wave equations in higher spatial dimensions0 aSobolev periodic solutions of nonlinear wave equations in higher a609-6420 v1953 aWe prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". © Springer-Verlag (2009).1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/sobolev-periodic-solutions-nonlinear-wave-equations-higher-spatial-dimensions00906nas a2200109 4500008004300000245009100043210006900134520052300203100001800726700001600744856003600760 2010 en_Ud 00aSolitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit0 aSolitonic asymptotics for the Kortewegde Vries equation in the s3 aWe 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.1 aGrava, Tamara1 aClaeys, Tom uhttp://hdl.handle.net/1963/383900741nas a2200133 4500008004100000245007400041210006900115260002400184300001100208490000700219520030000226100002200526856005900548 2010 eng d00aStable determination of an immersed body in a stationary Stokes fluid0 aStable determination of an immersed body in a stationary Stokes bIOP Publishingcnov a1250150 v263 aWe consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log–log type.

1 aBallerini, Andrea uhttps://doi.org/10.1088%2F0266-5611%2F26%2F12%2F12501500362nas a2200097 4500008004300000245007600043210006900119100002000188700002000208856003600228 2009 en_Ud 00aOn a Sobolev type inequality related to the weighted p-Laplace operator0 aSobolev type inequality related to the weighted pLaplace operato1 aGazzini, Marita1 aMusina, Roberta uhttp://hdl.handle.net/1963/261300857nas a2200133 4500008004100000245010700041210007200148300001200220490000700232520040100239100002000640700001700660856004600677 2009 eng d00aSolutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions0 aSolutions of the Schrödinger–Poisson problem concentrating on sp a707-7200 v193 aIn this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

1 aIanni, Isabella1 aVaira, Giusi uhttps://doi.org/10.1142/S021820250900358900350nas a2200097 4500008004300000245006900043210006900112260001300181100002200194856003600216 2009 en_Ud 00aSome new entire solutions of semilinear elliptic equations on Rn0 aSome new entire solutions of semilinear elliptic equations on Rn bElsevier1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/364500893nas a2200109 4500008004300000245007600043210006900119520051500188100002200703700002200725856003600747 2009 en_Ud 00aStrain-order coupling in nematic elastomers: equilibrium configurations0 aStrainorder coupling in nematic elastomers equilibrium configura3 aWe 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.1 aCesana, Pierluigi1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/270000754nas a2200121 4500008004300000245007200043210006900115520035700184100002200541700001600563700001700579856003600596 2009 en_Ud 00aStratos: a code for 3D free surface flows with floating constraints0 aStratos a code for 3D free surface flows with floating constrain3 aThis 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......1 aDeSimone, Antonio1 aBianchi, B.1 aHeltai, Luca uhttp://hdl.handle.net/1963/370101111nas a2200121 4500008004300000245007200043210006900115520069700184100002200881700002500903700002500928856003600953 2008 en_Ud 00aA second order minimality condition for the Mumford-Shah functional0 asecond order minimality condition for the MumfordShah functional3 aA 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.1 aCagnetti, Filippo1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/195501262nas a2200121 4500008004300000245007100043210006800114260002800182520085700210100002101067700001601088856003601104 2008 en_Ud 00aOn semistable principal bundles over a complex projective manifold0 asemistable principal bundles over a complex projective manifold bOxford University Press3 aLet 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.1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/341800611nas a2200121 4500008004300000245008600043210006900129520019400198100002400392700002100416700001600437856003600453 2008 en_Ud 00aSolitons of linearly coupled systems of semilinear non-autonomous equations on Rn0 aSolitons of linearly coupled systems of semilinear nonautonomous3 aUsing concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations.1 aAmbrosetti, Antonio1 aCerami, Giovanna1 aRuiz, David uhttp://hdl.handle.net/1963/217500349nas a2200097 4500008004300000245006900043210006800112100001700180700001800197856003600215 2008 en_Ud 00aStability of planar switched systems: the nondiagonalizable case0 aStability of planar switched systems the nondiagonalizable case1 aBoscain, Ugo1 aBalde, Moussa uhttp://hdl.handle.net/1963/185701518nas a2200109 4500008004300000245007900043210006900122520114200191100001701333700002201350856003601372 2008 en_Ud 00aSymmetric obstruction theories and Hilbert schemes of points on threefolds0 aSymmetric obstruction theories and Hilbert schemes of points on 3 aIn 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.1 aBehrend, Kai1 aFantechi, Barbara uhttp://hdl.handle.net/1963/270900905nas a2200121 4500008004100000245006700041210006700108260001000175520051900185653002600704100001700730856003600747 2008 en d00aSymmetries of noncommutative spaces and equivariant cohomology0 aSymmetries of noncommutative spaces and equivariant cohomology bSISSA3 aAs the title suggests, the main subject of this thesis is the study of symmetries of noncommutative spaces and related equivariant cohomologies. We focus on deformations of classical geometries coming from the action of some symmetry. A close relation between the deformation of the symmetry and the deformation of the space on which it acts is at the heart of our approach; we will use this idea to generate noncommutative geometries, and to de¯ne algebraic models for the equivariant cohomology of such actions.10aNoncommutative spaces1 aCirio, Lucio uhttp://hdl.handle.net/1963/525400296nas a2200097 4500008004300000245003900043210003900082100001600121700002500137856003600162 2007 en_Ud 00aSemistable principal Higgs bundles0 aSemistable principal Higgs bundles1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/253300729nas a2200121 4500008004300000245002700043210002700070520041600097100002200513700001800535700001800553856003600571 2007 en_Ud 00aSmooth toric DM stacks0 aSmooth toric DM stacks3 aWe 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.1 aFantechi, Barbara1 aMann, Etienne1 aNironi, Fabio uhttp://hdl.handle.net/1963/212000945nas a2200121 4500008004300000245006300043210006300106520056100169100002200730700001700752700001800769856003600787 2007 en_Ud 00aSoft elasticity and microstructure in smectic C elastomers0 aSoft elasticity and microstructure in smectic C elastomers3 aSmectic 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.1 aDeSimone, Antonio1 aAdams, James1 aConti, Sergio uhttp://hdl.handle.net/1963/181100726nas a2200097 4500008004300000245009800043210006900141520036200210100002000572856003600592 2007 en_Ud 00aSolutions of vectorial Hamilton-Jacobi equations and minimizers of nonquasiconvex functionals0 aSolutions of vectorial HamiltonJacobi equations and minimizers o3 aWe 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.1 aZagatti, Sandro uhttp://hdl.handle.net/1963/276301231nas a2200109 4500008004300000245012500043210006900168520080600237100002001043700002201063856003601085 2007 en_Ud 00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe 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.1 aMahmoudi, Fethi1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/211101499nas a2200121 4500008004300000245014300043210006900186520102000255100002001275700002201295700002401317856003601341 2007 en_Ud 00aSolutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions0 aSolutions to the nonlinear Schroedinger equation carrying moment3 aWe 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.1 aMahmoudi, Fethi1 aMalchiodi, Andrea1 aMontenegro, Marcelo uhttp://hdl.handle.net/1963/211200914nas a2200109 4500008004300000245006600043210006600109520054400175100002200719700002700741856003600768 2007 en_Ud 00aSome existence results for the Toda system on closed surfaces0 aSome existence results for the Toda system on closed surfaces3 aGiven 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 $\\\\rho_2 < 4 \\\\pi$.1 aMalchiodi, Andrea1 aNdiaye, Cheikh Birahim uhttp://hdl.handle.net/1963/177500406nas a2200097 4500008004300000245011700043210006900160100001900229700002400248856003600272 2007 en_Ud 00aStability of front tracking solutions to the initial and boundary value problem for systems of conservation laws0 aStability of front tracking solutions to the initial and boundar1 aMarson, Andrea1 aDonadello, Carlotta uhttp://hdl.handle.net/1963/176900537nas a2200109 4500008004300000245006800043210006800111520016600179100002400345700002200369856003600391 2007 en_Ud 00aStanding waves of some coupled Nonlinear Schrödinger Equations0 aStanding waves of some coupled Nonlinear Schrödinger Equations3 aWe 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.1 aAmbrosetti, Antonio1 aColorado, Eduardo uhttp://hdl.handle.net/1963/182100738nas a2200097 4500008004300000245008700043210006900130520037600199100002900575856003600604 2007 en_Ud 00aStrengthened convergence of marginals to the cubic nonlinear Schroedinger equation0 aStrengthened convergence of marginals to the cubic nonlinear Sch3 aWe 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.1 aMichelangeli, Alessandro uhttp://hdl.handle.net/1963/197700907nas a2200121 4500008004300000245005500043210005300098520053100151100001900682700002500701700002300726856003600749 2007 en_Ud 00aSurfactants in Foam Stability: A Phase-Field Model0 aSurfactants in Foam Stability A PhaseField Model3 aThe 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.1 aFonseca, Irene1 aMorini, Massimiliano1 aSlastikov, Valeriy uhttp://hdl.handle.net/1963/203500554nas a2200145 4500008004100000022001400041245008800055210006900143300001400212490000800226100001900234700001500253700001500268856012500283 2006 eng d a0010-361600aSemiclassical orthogonal polynomials, matrix models and isomonodromic tau functions0 aSemiclassical orthogonal polynomials matrix models and isomonodr a401–4370 v2631 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://www.math.sissa.it/publication/semiclassical-orthogonal-polynomials-matrix-models-and-isomonodromic-tau-functions01043nas a2200109 4500008004300000245005700043210005400100520069600154100001600850700003100866856003600897 2006 en_Ud 00aSemistability vs. nefness for (Higgs) vector bundles0 aSemistability vs nefness for Higgs vector bundles3 aAccording 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.1 aBruzzo, Ugo1 aHernandez Ruiperez, Daniel uhttp://hdl.handle.net/1963/223700519nas a2200109 4500008004300000245006800043210006300111520016100174100002100335700001700356856003600373 2006 en_Ud 00aOn Separation of Variables for Homogeneous SL(r) Gaudin Systems0 aSeparation of Variables for Homogeneous SLr Gaudin Systems3 aBy 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.1 aFalqui, Gregorio1 aMusso, Fabio uhttp://hdl.handle.net/1963/253801217nas a2200097 4500008004300000245004300043210004200086520093100128100002401059856003601083 2006 en_Ud 00aSpectral geometry of k-Minkowski space0 aSpectral geometry of kMinkowski space3 aAfter recalling Snyder's idea of using vector fields over a smooth manifold as "coordinates on a noncommutative space", we discuss a two dimensional toy-model whose "dual" noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its "spectral properties" and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.

1 aD'Andrea, Francesco uhttp://hdl.handle.net/1963/213100968nas a2200121 4500008004300000245005100043210005100094520060400145100001700749700002300766700002100789856003600810 2006 en_Ud 00aStability of planar nonlinear switched systems0 aStability of planar nonlinear switched systems3 aWe consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields.1 aBoscain, Ugo1 aCharlot, Grégoire1 aSigalotti, Mario uhttp://hdl.handle.net/1963/171001313nas a2200133 4500008004300000245008200043210006900125260001300194520087600207100001801083700002201101700002001123856003601143 2005 en_Ud 00aSelf-similar folding patterns and energy scaling in compressed elastic sheets0 aSelfsimilar folding patterns and energy scaling in compressed el bElsevier3 aThin 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.1 aConti, Sergio1 aDeSimone, Antonio1 aMüller, Stefan uhttp://hdl.handle.net/1963/300000333nas a2200109 4500008004300000020001800043245004400061210004200105100001700147700002300164856003600187 2005 en_Ud a2 7056 6511 000aA short introduction to optimal control0 ashort introduction to optimal control1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/225700351nas a2200085 4500008004300000245009600043210006900139100002100208856003600229 2005 en_Ud 00aSolutions of Neumann problems in domains with cracks and applications to fracture mechanics0 aSolutions of Neumann problems in domains with cracks and applica1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/168400730nas a2200133 4500008004300000245005800043210005400101520032400155100002200479700002000501700001900521700002000540856003600560 2005 en_Ud 00aThe spectral geometry of the equatorial Podles sphere0 aspectral geometry of the equatorial Podles sphere3 aWe 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.1 aDabrowski, Ludwik1 aLandi, Giovanni1 aPaschke, Mario1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/227501445nas a2200121 4500008004300000245006200043210006200105260001300167520106100180100002801241700001801269856003601287 2005 en_Ud 00aStability of solutions of quasilinear parabolic equations0 aStability of solutions of quasilinear parabolic equations bElsevier3 aWe 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.1 aCoclite, Giuseppe Maria1 aHolden, Helge uhttp://hdl.handle.net/1963/289201246nas a2200109 4500008004300000245010500043210006900148520083800217100002201055700002301077856003601100 2005 en_Ud 00aStress-dilatancy based modelling of granular materials and extensions to soils with crushable grains0 aStressdilatancy based modelling of granular materials and extens3 aStress-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.1 aDeSimone, Antonio1 aTamagnini, Claudio uhttp://hdl.handle.net/1963/216500849nas a2200121 4500008004300000245005800043210005800101260001900159520046100178100002900639700002300668856003600691 2004 en_Ud 00aSemiclassical analysis of constrained quantum systems0 aSemiclassical analysis of constrained quantum systems bIOP Publishing3 aWe 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.1 aDell'Antonio, Gianfausto1 aTenuta, Lucattilio uhttp://hdl.handle.net/1963/299701056nas a2200121 4500008004300000245005500043210005400098260001300152520069800165100002100863700001400884856003600898 2004 en_Ud 00aSemi-cooperative strategies for differential games0 aSemicooperative strategies for differential games bSpringer3 aThe 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.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/289300741nas a2200121 4500008004300000245005600043210005400099260000900153520038500162100002100547700001500568856003600583 2004 en_Ud 00aA sharp decay estimate for positive nonlinear waves0 asharp decay estimate for positive nonlinear waves bSIAM3 aWe 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.1 aBressan, Alberto1 aYang, Tong uhttp://hdl.handle.net/1963/291601974nas a2200109 4500008004300000245009900043210006900142520157600211100002301787700001801810856003601828 2004 en_Ud 00aSingular Z_N curves, Riemann-Hilbert problem and modular solutions of the Schlesinger equation0 aSingular ZN curves RiemannHilbert problem and modular solutions 3 aWe 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.1 aEnolski, Victor Z.1 aGrava, Tamara uhttp://hdl.handle.net/1963/254000490nas a2200121 4500008004100000245011600041210006900157260004300226100002400269700002200293700001700315856003600332 2004 en d00aSingularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II0 aSingularity perturbed elliptic equations with symmetry existence bIndiana University Mathematics Journal1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/166300818nas a2200121 4500008004300000245007100043210006900114260000900183520043300192100002100625700001400646856003600660 2004 en_Ud 00aSmall BV solutions of hyperbolic noncooperative differential games0 aSmall BV solutions of hyperbolic noncooperative differential gam bSIAM3 aThe 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.1 aBressan, Alberto1 aShen, Wen uhttp://hdl.handle.net/1963/291700759nas a2200121 4500008004100000245005300041210005300094260001800147520038500165100002800550700002300578856003600601 2004 en d00aSolitary waves for Maxwell Schrodinger equations0 aSolitary waves for Maxwell Schrodinger equations bSISSA Library3 aIn 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.1 aCoclite, Giuseppe Maria1 aGeorgiev, Vladimir uhttp://hdl.handle.net/1963/158200365nas a2200097 4500008004100000245008600041210006900127260001300196100002200209856003600231 2004 en d00aSolutions concentrating at curves for some singularly perturbed elliptic problems0 aSolutions concentrating at curves for some singularly perturbed bElsevier1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/486900322nas a2200097 4500008004100000245004600041210004600087260003100133100002400164856003600188 2004 en d00aSoluzioni periodiche di PDEs Hamiltoniane0 aSoluzioni periodiche di PDEs Hamiltoniane bUnione Matematica Italiana1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/458200736nas a2200109 4500008004300000245006600043210006600109260003500175520035900210100002100569856003600590 2004 en_Ud 00aSome remarks on multidimensional systems of conservation laws0 aSome remarks on multidimensional systems of conservation laws bAccademia Nazionale dei Lincei3 aThis 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.1 aBressan, Alberto uhttp://hdl.handle.net/1963/364200882nas a2200121 4500008004300000245004500043210004500088260001700133520053500150100001800685700002100703856003600724 2004 en_Ud 00aStability rates for patchy vector fields0 aStability rates for patchy vector fields bEDP Sciences3 aThis 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.1 aAncona, Fabio1 aBressan, Alberto uhttp://hdl.handle.net/1963/295900859nas a2200121 4500008004300000245007000043210006900113260001300182520046800195100001600663700002200679856003600701 2004 en_Ud 00aSuperlocalization formulas and supersymmetric Yang-Mills theories0 aSuperlocalization formulas and supersymmetric YangMills theories bElsevier3 aBy 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.1 aBruzzo, Ugo1 aFucito, Francesco uhttp://hdl.handle.net/1963/288600432nas a2200109 4500008004100000022001400041245006300055210006200118300002900180100001900209856009400228 2003 eng d a1126-670800aSecond and third order observables of the two-matrix model0 aSecond and third order observables of the twomatrix model a062, 30 pp. (electronic)1 aBertola, Marco uhttps://www.math.sissa.it/publication/second-and-third-order-observables-two-matrix-model00998nas a2200121 4500008004100000245005500041210005400096260001800150520063200168100002100800700001900821856003600840 2003 en d00aSeparation of variables for Bi-Hamiltonian systems0 aSeparation of variables for BiHamiltonian systems bSISSA Library3 aWe 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.1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/159800579nas a2200109 4500008004300000245008900043210006900132260000900201520019800210100002500408856003600433 2003 en_Ud 00aSequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems0 aSequences of Singularly Perturbed Functionals Generating FreeDis bSIAM3 aWe 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.1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/307100397nas a2200097 4500008004100000245012200041210006900163260001000232100002100242856003600263 2003 en d00aSingle-Input Control Affine Systems: Local Regularity of Optimal Trajectories and a Geometric Controllability Problem0 aSingleInput Control Affine Systems Local Regularity of Optimal T bSISSA1 aSigalotti, Mario uhttp://hdl.handle.net/1963/534200459nas a2200121 4500008004100000245011500041210006900156260001300225100002400238700002200262700001700284856003600301 2003 en d00aSingularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I0 aSingularly perturbed elliptic equations with symmetry existence bSpringer1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/163300426nas a2200121 4500008004100000245007300041210006900114260001800183100002100201700001800222700002800240856003600268 2003 en d00aSome results on the boundary control of systems of conservation laws0 aSome results on the boundary control of systems of conservation bSISSA Library1 aBressan, Alberto1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/161501403nas a2200133 4500008004300000245004000043210003900083260002400122520102800146100002101174700001901195700001901214856003601233 2003 en_Ud 00aSpace-adiabatic perturbation theory0 aSpaceadiabatic perturbation theory bInternational Press3 aWe study approximate solutions to the Schr\\\\\\\"odinger equation $i\\\\epsi\\\\partial\\\\psi_t(x)/\\\\partial t = H(x,-i\\\\epsi\\\\nabla_x) \\\\psi_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of bounded operators on the Hilbert space $\\\\Hi_{\\\\rm f}$ of fast ``internal\\\'\\\' degrees of freedom. By assumption $H(q,p)$ has an isolated energy band. Using a method of Nenciu and Sordoni \\\\cite{NS} we prove that interband transitions are suppressed to any order in $\\\\epsi$. As a consequence, associated to that energy band there exists a subspace of $L^2(\\\\mathbb{R}^d,\\\\Hi _{\\\\rm f})$ almost invariant under the unitary time evolution. We develop a systematic perturbation scheme for the computation of effective Hamiltonians which govern approximately the intraband time evolution. As examples for the general perturbation scheme we discuss the Dirac and Born-Oppenheimer type Hamiltonians and we reconsider also the time-adiabatic theory.1 aPanati, Gianluca1 aSpohn, Herbert1 aTeufel, Stefan uhttp://hdl.handle.net/1963/304100672nas a2200133 4500008004100000245008000041210006900121260001800190520022400208100002100432700002300453700002600476856003600502 2003 en d00aA stability result for nonlinear Neumann problems under boundary variations0 astability result for nonlinear Neumann problems under boundary v bSISSA Library3 aIn 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.1 aDal Maso, Gianni1 aEbobisse, Francois1 aPonsiglione, Marcello uhttp://hdl.handle.net/1963/161800355nas a2200097 4500008004100000245007800041210006700119260001300186100002200199856003600221 2002 en d00aThe scalar curvature problem on $S\\\\sp n$: an approach via Morse theory0 ascalar curvature problem on Ssp n an approach via Morse theory bSpringer1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/133100345nas a2200109 4500008004100000245005200041210005200093260001100145100002100156700002200177856003600199 2002 en d00aSingular elliptic problems with critical growth0 aSingular elliptic problems with critical growth bDekker1 aCaldiroli, Paolo1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/126800585nas a2200133 4500008004100000245008200041210006900123260001800192520014200210100002400352700002200376700001700398856003600415 2002 en d00aSolutions concentrating on spheres to symmetric singularly perturbed problems0 aSolutions concentrating on spheres to symmetric singularly pertu bSISSA Library3 aWe discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere.1 aAmbrosetti, Antonio1 aMalchiodi, Andrea1 aNi, Wei-Ming uhttp://hdl.handle.net/1963/159400307nas a2200097 4500008004100000245005100041210005000092260001000142100002100152856003600173 2002 en d00aSpace-adiabatic Decoupling in Quantum Dynamics0 aSpaceadiabatic Decoupling in Quantum Dynamics bSISSA1 aPanati, Gianluca uhttp://hdl.handle.net/1963/636001131nas a2200133 4500008004100000245006000041210005900101260003000160520071200190100002100902700001900923700001900942856003600961 2002 en d00aSpace-adiabatic perturbation theory in quantum dynamics0 aSpaceadiabatic perturbation theory in quantum dynamics bAmerican Physical Society3 aA systematic perturbation scheme is developed for approximate solutions to the time-dependent Schrödinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from dynamics. The kinematics is defined through a subspace of the full Hilbert space for which transitions to other band subspaces are suppressed to all orders, and the dynamics operates in that subspace in terms of an effective intraband Hamiltonian. As novel applications, we discuss the Born-Oppenheimer theory to second order and derive for the first time the nonperturbative definition of the g factor of the electron within nonrelativistic quantum electrodynamics.1 aPanati, Gianluca1 aSpohn, Herbert1 aTeufel, Stefan uhttp://hdl.handle.net/1963/598501393nas a2200109 4500008004100000245007100041210006900112260000900181520104000190100001701230856003601247 2002 en d00aStability of planar switched systems: the linear single input case0 aStability of planar switched systems the linear single input cas bSIAM3 aWe study the stability of the origin for the dynamical system $\\\\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where A and B are two 2 × 2 real matrices with eigenvalues having strictly negative real part, $x\\\\in {\\\\mbox{{\\\\bf R}}}^2$, and $u(.):[0,\\\\infty[\\\\to[0,1]$ is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). The result is obtained without looking for a common Lyapunov function but studying the locus in which the two vector fields Ax and Bx are collinear. There are only three relevant parameters: the first depends only on the eigenvalues of A, the second depends only on the eigenvalues of B, and the third contains the interrelation among the two systems, and it is the cross ratio of the four eigenvectors of A and B in the projective line CP1. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied.1 aBoscain, Ugo uhttp://hdl.handle.net/1963/152900355nas a2200109 4500008004100000245005500041210004800096260001800144100002300162700002400185856003600209 2002 en d00aOn the Stability of the Standard Riemann Semigroup0 aStability of the Standard Riemann Semigroup bSISSA Library1 aBianchini, Stefano1 aColombo, Rinaldo M. uhttp://hdl.handle.net/1963/152800395nas a2200109 4500008004100000245008300041210006900124260001500193100002100208700002000229856003600249 2001 en d00aS^2 type parametric surfaces with prescribed mean curvature and minimal energy0 aS2 type parametric surfaces with prescribed mean curvature and m bBirkhauser1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/160500970nas a2200121 4500008004300000245007300043210006500116260003100181520055000212100002800762700002200790856003600812 2001 en_Ud 00aOn the spreading of characteristics for non-convex conservation laws0 aspreading of characteristics for nonconvex conservation laws bCambridge University Press3 aWe study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos\\\' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an Hölder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution.1 aJenssen, Helge Kristian1 aSinestrari, Carlo uhttp://hdl.handle.net/1963/326501077nas a2200109 4500008004100000245010100041210006900142260001800211520067900229100002300908856003600931 2001 en d00aStability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions0 aStability of Linfinity solutions for hyperbolic systems with coi bSISSA Library3 aWe 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.1 aBianchini, Stefano uhttp://hdl.handle.net/1963/152300389nas a2200109 4500008004100000245007400041210006900115260001800184100002100202700002000223856003600243 2001 en d00aStationary states for a two-dimensional singular Schrodinger equation0 aStationary states for a twodimensional singular Schrodinger equa bSISSA Library1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/124900364nas a2200109 4500008004100000245005900041210005100100260001800151100002500169700002400194856003600218 2001 en d00aOn the subanalyticity of Carnot-Caratheodory distances0 asubanalyticity of CarnotCaratheodory distances bSISSA Library1 aAgrachev, Andrei, A.1 aGauthier, Jean-Paul uhttp://hdl.handle.net/1963/148300499nas a2200121 4500008004300000245005900043210004800102260001300150520013200163100002400295700002200319856003600341 2001 en_Ud 00aOn the symmetric scalar curvature problem on S\\\\sp n0 asymmetric scalar curvature problem on Ssp n bElsevier3 aWe discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries.1 aAmbrosetti, Antonio1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/309500372nas a2200121 4500008004100000245004700041210004700088260001800135100002400153700001500177700002200192856003600214 2000 en d00aScalar curvature under boundary conditions0 aScalar curvature under boundary conditions bSISSA Library1 aAmbrosetti, Antonio1 aYanYan, Li1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/150600824nas a2200109 4500008004300000245008300043210006900126260002300195520043700218100002300655856003600678 2000 en_Ud 00aThe semigroup generated by a Temple class system with non-convex flux function0 asemigroup generated by a Temple class system with nonconvex flux bKhayyam Publishing3 aWe consider the Cauchy problem for a nonlinear n × n system of conservation laws of Temple class, i.e. with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation.1 aBianchini, Stefano uhttp://hdl.handle.net/1963/322100416nas a2200097 4500008004100000245010100041210006900142260004800211100002300259856003600282 2000 en d00aOn the shift differentiability of the flow generated by a hyperbolic system of conservation laws0 ashift differentiability of the flow generated by a hyperbolic sy bAmerican Institute of Mathematical Sciences1 aBianchini, Stefano uhttp://hdl.handle.net/1963/127400945nas a2200133 4500008004100000245007400041210006900115260001800184520050900202100002200711700002200733700002000755856003600775 2000 en d00aSome Properties of Non-linear sigma-Models in Noncommutative Geometry0 aSome Properties of Nonlinear sigmaModels in Noncommutative Geome bSISSA Library3 aWe 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.1 aDabrowski, Ludwik1 aKrajewski, Thomas1 aLandi, Giovanni uhttp://hdl.handle.net/1963/137300947nas a2200121 4500008004300000245005900043210005800102260002300160520056700183100002100750700001800771856003600789 2000 en_Ud 00aStability of L^infty Solutions of Temple Class Systems0 aStability of Linfty Solutions of Temple Class Systems bKhayyam Publishing3 aLet $u_t+f(u)_x=0$ 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.

1 aBressan, Alberto1 aGoatin, Paola uhttp://hdl.handle.net/1963/325600401nas a2200109 4500008004100000245008600041210006900127260001800196100002000214700002100234856003600255 2000 en d00aOn a Steffen\\\'s result about parametric surfaces with prescribed mean curvature0 aSteffens result about parametric surfaces with prescribed mean c bSISSA Library1 aMusina, Roberta1 aCaldiroli, Paolo uhttp://hdl.handle.net/1963/155800604nas a2200133 4500008004100000020001800041245007300059210007000132260002700202520016100229653002300390100002100413856003600434 2000 en d a4-907719-07-800aStokes Matrices for Frobenius Manifolds and the 6 Painlevé Equation0 aStokes Matrices for Frobenius Manifolds and the 6 Painlevé Equat bKobe University, Japan3 aThese notes are a short review on the theory of Frobenius manifolds and its connection to problems of isomonodromy deformations and to Painlev'e equations.10aPainlevé equation1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/654600454nas a2200121 4500008004100000245010700041210006900148260001800217100002100235700001800256700002200274856003600296 2000 en d00aSuper KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy0 aSuper KP equations and Darboux transformations another perspecti bSISSA Library1 aFalqui, Gregorio1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/136700346nas a2200109 4500008004100000245005100041210004400092260001800136100002400154700002200178856003600200 1999 en d00aOn the scalar curvature problem under symmetry0 ascalar curvature problem under symmetry bSISSA Library1 aAmbrosetti, Antonio1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/128700363nas a2200097 4500008004100000245007600041210006900117100002200186700002100208856003600229 1999 en d00aSome properties of the solutions of obstacle problems with measure data0 aSome properties of the solutions of obstacle problems with measu1 aDall'Aglio, Paolo1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/643200949nas a2200109 4500008004300000245008100043210006900124260001300193520057600206100002100782856003600803 1999 en_Ud 00aStokes matrices and monodromy of the quantum cohomology of projective spaces0 aStokes matrices and monodromy of the quantum cohomology of proje bSpringer3 an 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.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/347500739nas a2200121 4500008004300000245010400043210006900147260002300216520029600239100002100535700002500556856003600581 1999 en_Ud 00aStructural stability and regularity of entropy solutions to hyperbolic systems of conservation laws0 aStructural stability and regularity of entropy solutions to hype bIndiana University3 aThe 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.1 aBressan, Alberto1 aLeFloch, Philippe G. uhttp://hdl.handle.net/1963/337400446nas a2200121 4500008004100000245009900041210006900140260001800209100002000227700002000247700002100267856003600288 1998 en d00aSpecial functions with bounded variation and with weakly differentiable traces on the jump set0 aSpecial functions with bounded variation and with weakly differe bSISSA Library1 aAmbrosio, Luigi1 aBraides, Andrea1 aGarroni, Adriana uhttp://hdl.handle.net/1963/102500841nas a2200121 4500008004100000245006900041210006500110260001800175520045200193100001700645700002100662856003600683 1997 en d00aThe semigroup generated by a temple class system with large data0 asemigroup generated by a temple class system with large data bSISSA Library3 aWe 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.1 aBaiti, Paolo1 aBressan, Alberto uhttp://hdl.handle.net/1963/102300768nas a2200121 4500008004100000245007200041210006900113260001800182520036800200100002100568700002100589856003600610 1997 en d00aShift-differentiability of the flow generated by a conservation law0 aShiftdifferentiability of the flow generated by a conservation l bSISSA Library3 aThe 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.1 aBressan, Alberto1 aGuerra, Graziano uhttp://hdl.handle.net/1963/103300409nas a2200109 4500008004100000245010100041210006900142260001000211653002300221100001900244856003600263 1997 en d00aSome Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains0 aSome Problems in the Asymptotic Analysis of Partial Differential bSISSA10aDirichlet problems1 aToader, Rodica uhttp://hdl.handle.net/1963/569800401nas a2200109 4500008004100000245009300041210006900134260001000203100002100213700002100234856003600255 1997 en d00aSome properties of reachable solutions of nonlinear elliptic equations with measure data0 aSome properties of reachable solutions of nonlinear elliptic equ bSISSA1 aDal Maso, Gianni1 aMalusa, Annalisa uhttp://hdl.handle.net/1963/643401073nas a2200133 4500008004100000245003800041210003800079260001800117520069900135100002900834700002000863700002100883856003500904 1997 en d00aStatistics in space dimension two0 aStatistics in space dimension two bSISSA Library3 aWe 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).1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/13000363nas a2200109 4500008004100000245005800041210005700099260001800156100002100174700002300195856003500218 1997 en d00aStructural stability for time-optimal planar sytheses0 aStructural stability for timeoptimal planar sytheses bSISSA Library1 aBressan, Alberto1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/99700349nas a2200097 4500008004100000245005900041210005500100260003900155100002100194856003600215 1996 en d00aThe semigroup approach to systems of conservation laws0 asemigroup approach to systems of conservation laws bSociedade Brasileira de Matematica1 aBressan, Alberto uhttp://hdl.handle.net/1963/103700352nas a2200097 4500008004100000245006800041210006800109260001800177100002400195856003500219 1996 en d00aSolving Honig generic problem about Volterra integral equations0 aSolving Honig generic problem about Volterra integral equations bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/94100558nas a2200109 4500008004100000245004300041210004300084260000900127520025400136100002300390856003500413 1995 en d00aSome control problems for the pendulum0 aSome control problems for the pendulum bIEEE3 aThe 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.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/98200375nas a2200121 4500008004100000245004500041210004500086260001800131100002500149700002300174700002100197856003500218 1995 en d00aSpecial functions of bounded deformation0 aSpecial functions of bounded deformation bSISSA Library1 aBellettini, Giovanni1 aCoscia, Alessandra1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/97800348nas a2200109 4500008004100000245005200041210005200093260001000145653002700155100002000182856003600202 1992 en d00aSome Problems in the Calculus of the Variations0 aSome Problems in the Calculus of the Variations bSISSA10aCalculus of variations1 aZagatti, Sandro uhttp://hdl.handle.net/1963/542800410nas a2200109 4500008004100000245009300041210006900134260001800203100002300221700002100244856003500265 1991 en d00aShape optimization for Dirichlet problems: relaxed formulations and optimally conditions0 aShape optimization for Dirichlet problems relaxed formulations a bSISSA Library1 aButtazzo, Giuseppe1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/88000391nas a2200109 4500008004100000245007600041210006900117260001800186100002100204700002100225856003500246 1991 en d00aOn systems of ordinary differential equations with measures as controls0 asystems of ordinary differential equations with measures as cont bSISSA Library1 aDal Maso, Gianni1 aRampazzo, Franco uhttp://hdl.handle.net/1963/84000408nas a2200109 4500008004100000245009100041210006900132260001800201100002300219700002100242856003500263 1990 en d00aShape optimization for Dirichlet problems: relaxed solutions and optimality conditions0 aShape optimization for Dirichlet problems relaxed solutions and bSISSA Library1 aButtazzo, Giuseppe1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/80900362nas a2200097 4500008004100000245008700041210006900128260001000197100002100207856003600228 1989 en d00aSingular perturbation of the Laplacian and connections with models of random media0 aSingular perturbation of the Laplacian and connections with mode bSISSA1 aTeta, Alessandro uhttp://hdl.handle.net/1963/634800402nas a2200097 4500008004100000245011700041210006900158260001800227100002400245856003500269 1989 en d00aOn the solvability of boundary value problems for higher order ordinary differential equations (Revised version)0 asolvability of boundary value problems for higher order ordinary bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/66200384nas a2200097 4500008004100000245009900041210006900140260001800209100002400227856003500251 1989 en d00aOn the solvability of boundary value problems for higher order ordinary differential equations0 asolvability of boundary value problems for higher order ordinary bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/63100374nas a2200109 4500008004100000245006700041210006100108260001800169100002200187700002000209856003500229 1989 en d00aSurfaces of minimal area enclosing a given body in R\\\\sp 3.0 aSurfaces of minimal area enclosing a given body in Rsp 3 bSISSA Library1 aMancini, Giovanni1 aMusina, Roberta uhttp://hdl.handle.net/1963/61900392nas a2200109 4500008004100000245007100041210006800112260001800180100002100198700002800219856003500247 1988 en d00aSome properties of a class of nonlinear variational $m$-capacities0 aSome properties of a class of nonlinear variational mcapacities bSISSA Library1 aDal Maso, Gianni1 aDefranceschi, Anneliese uhttp://hdl.handle.net/1963/48500306nas a2200109 4500008004100000245003200041210003100073260001800104100002100122700001800143856003500161 1988 en d00aSusy-curves and supermoduli0 aSusycurves and supermoduli bSISSA Library1 aFalqui, Gregorio1 aReina, Cesare uhttp://hdl.handle.net/1963/76100402nas a2200109 4500008004100000245007900041210006900120260001800189100002400207700002600231856003500257 1987 en d00aSolutions with minimal period for Hamiltonian systems in a potential well.0 aSolutions with minimal period for Hamiltonian systems in a poten bSISSA Library1 aAmbrosetti, Antonio1 aCoti Zelati, Vittorio uhttp://hdl.handle.net/1963/46600374nas a2200121 4500008004100000245004500041210004500086260001800131100002400149700002600173700001800199856003500217 1987 en d00aSymmetry breaking in Hamiltonian systems0 aSymmetry breaking in Hamiltonian systems bSISSA Library1 aAmbrosetti, Antonio1 aCoti Zelati, Vittorio1 aEkeland, Ivar uhttp://hdl.handle.net/1963/40900386nas a2200097 4500008004100000245010400041210006900145260001800214100002100232856003500253 1985 en d00aSome necessary and sufficient conditions for the convergence of sequences of unilateral convex sets0 aSome necessary and sufficient conditions for the convergence of bSISSA Library1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/31800353nas a2200097 4500008004100000245007100041210006900112260001800181100002100199856003500220 1985 en d00aSome singular perturbation problems in the calculus of variations.0 aSome singular perturbation problems in the calculus of variation bSISSA Library1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/29700345nas a2200109 4500008004100000245005700041210005700098260001000155653001200165100002200177856003600199 1984 en d00aSpin Structures and Global Conformal Transformations0 aSpin Structures and Global Conformal Transformations bSISSA10aSpinors1 aDabrowski, Ludwik uhttp://hdl.handle.net/1963/5854