Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.

%B Calculus of Variations and Partial Differential Equations %V 55 %P 17 %8 Jan %G eng %U https://doi.org/10.1007/s00526-015-0947-6 %R 10.1007/s00526-015-0947-6 %0 Journal Article %J arXiv preprint arXiv:1602.08745 %D 2016 %T Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics %A Andrei A. Agrachev %A Davide Barilari %A Elisa Paoli %B arXiv preprint arXiv:1602.08745 %G eng %0 Thesis %D 2015 %T Variational aspects of Liouville equations and systems %A Aleks Jevnikar %K Toda system %I SISSA %G en %1 34676 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by ajevnika@sissa.it (ajevnika@sissa.it) on 2015-08-08T16:04:38Z No. of bitstreams: 1 tesi phd.pdf: 1034249 bytes, checksum: 6988a3a6220b4d1bbd38c3124f520655 (MD5) %0 Thesis %D 2015 %T Variational aspects of singular Liouville systems %A Luca Battaglia %K Variational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods %X I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results. %I SISSA %G en %1 34737 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by lbatta@sissa.it (lbatta@sissa.it) on 2015-09-22T09:49:56Z No. of bitstreams: 1 thesis0.pdf: 1795685 bytes, checksum: e981358904223d6649e47eb70e6da429 (MD5) %0 Thesis %D 2015 %T Volume variation and heat kernel for affine control problems %A Elisa Paoli %K Heat kernel asymptotics %X In this thesis we study two main problems. The first one is the small-time heat kernel expansion on the diagonal for second order hypoelliptic opeartors. We consider operators that can depend on a drift field and that satisfy only the weak Hörmander condition. In a first work we use perturbation techniques to determine the exact order of decay of the heat kernel, that depends on the Lie algebra generated by the fields involved in the hypoelliptic operator. We generalize in particular some results already obtained in the sub-Riemannian setting. In a second work we consider a model class of hypoelliptic operators and we characterize geometrically all the coefficients in the on-the diagonal asymptotics at the equilibrium points of the drift field. The class of operators that we consider contains the linear hypoelliptic operators with constant second order part on the Euclidean space. We describe the coefficients in terms only of the divergence of the drift field and of curvature-like invariants, related to the minimal cost of geodesics of the associated optimal control problem. In the second part of the thesis we consider the variation of a smooth volume along a geodesic. The structure of the manifold is induced by a quadratic Hamiltonian and the geodesic in described as the projection of the Hamiltonian flow. We find an expansion similar to the classical Riemannian one. It depends on the curvature operator associated to the Hamiltonian, on the symbol of the geodesic and on a new metric-measure invariant determined by the symbol of the geodesic and by the given volume. %I SISSA %G en %1 35290 %2 Mathematics %4 -1 %# MAT/05 %$ Submitted by epaoli@sissa.it (epaoli@sissa.it) on 2015-11-26T08:47:31Z No. of bitstreams: 1 Paoli_thesis.pdf: 1061974 bytes, checksum: d273a57f7bf44214d5fc30460ece686a (MD5) %0 Thesis %D 2014 %T A variational approach to statics and dynamics of elasto-plastic systems %A Riccardo Scala %K delamination %X We prove some existence results for dynamic evolutions in elasto-plasticity and delamination. We study the limit as the data vary very slowly and prove convergence results to quasistatic evolutions. We model dislocations by mean of currents, we introduce the space of deformations in the presence of dislocations and study the graphs of these maps. We prove existence results for minimum problems. We study the properties of minimizers. %I SISSA %G en_US %U http://urania.sissa.it/xmlui/handle/1963/7471 %1 7583 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Riccardo Scala (rscala@sissa.it) on 2014-10-29T12:04:30Z No. of bitstreams: 1 tesi.pdf: 1322338 bytes, checksum: 5fcf0395d13a0dc16eac4edaef440913 (MD5) %0 Journal Article %D 2014 %T A variational model for the quasi-static growth of fractional dimensional brittle fractures %A Simone Racca %A Rodica Toader %K Variational models %XWe propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

%I European Mathematical Society %G en %U http://hdl.handle.net/1963/6983 %1 6973 %2 Mathematics %4 -1 %$ Submitted by Simone Racca (sracca@sissa.it) on 2013-07-18T08:39:00Z No. of bitstreams: 1 Racca_Toader.pdf: 416939 bytes, checksum: cf459548a10944037e56b7504fe60f51 (MD5) %R 10.4171/IFB/328 %0 Journal Article %D 2014 %T Vortex Partition Functions, Wall Crossing and Equivariant Gromov–Witten Invariants %A Giulio Bonelli %A Antonio Sciarappa %A Alessandro Tanzini %A Petr Vasko %X In this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov–Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov–Witten theory follow just by deforming the integration contour. In particular, we apply our formalism to compute Gromov–Witten invariants of the C3/Zn orbifold, of the Uhlembeck (partial) compactification of the moduli space of instantons on C2, and of An and Dn singularities both in the orbifold and resolved phases. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algebrae. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34652 %1 34859 %2 Physics %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T12:25:03Z No. of bitstreams: 1 preprint2014.pdf: 652465 bytes, checksum: 355132ee06625045b6adf8b1f4862533 (MD5) %R 10.1007/s00220-014-2193-8 %0 Journal Article %J Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371 %D 2013 %T A variational Analysis of the Toda System on Compact Surfaces %A Andrea Malchiodi %A David Ruiz %X In this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2. %B Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371 %I Wiley %G en %U http://hdl.handle.net/1963/6558 %1 6489 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:26:34Z No. of bitstreams: 1 1105.3701v2.pdf: 306787 bytes, checksum: f64fe03fd72ea85831e8f8ca25e9f99e (MD5) %R 10.1002/cpa.21433 %0 Journal Article %J Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %D 2012 %T Variational implementation of immersed finite element methods %A Luca Heltai %A Francesco Costanzo %K Turbulent flow %XDirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

%B Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 %I Elsevier %G en %U http://hdl.handle.net/1963/6462 %1 6389 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Lucio Lubiana (lubiana@sissa.it) on 2013-02-04T16:21:56Z\\nNo. of bitstreams: 0 %R 10.1016/j.cma.2012.04.001 %0 Journal Article %J JHEP 06(2012)178 %D 2012 %T Vertices, vortices & interacting surface operators %A Giulio Bonelli %A Alessandro Tanzini %A Zhao Jian %X We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations. %B JHEP 06(2012)178 %I SISSA %G en %U http://hdl.handle.net/1963/4134 %1 3874 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T08:59:30Z\\r\\nNo. of bitstreams: 1\\r\\n1102.0184v1.pdf: 250685 bytes, checksum: b0209b95cc58d31e3cd28c41cd8b0f25 (MD5) %R 10.1007/JHEP06(2012)178 %0 Journal Article %J Advances in Calculus of Variations 5 (2012) 433-483 %D 2012 %T A Viscosity-driven crack evolution %A Simone Racca %XWe present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith’s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

%B Advances in Calculus of Variations 5 (2012) 433-483 %I SISSA %G en %U http://hdl.handle.net/1963/5130 %1 4944 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-11-29T07:47:42Z\\r\\nNo. of bitstreams: 1\\r\\n63M_Racca.pdf: 473110 bytes, checksum: f4d49c3f7e2b984e9694fbd66a806447 (MD5) %R 10.1515/acv-2011-0012 %0 Journal Article %J Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 %D 2009 %T A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions %A Gianni Dal Maso %A Alessandro Giacomini %A Marcello Ponsiglione %B Boll. Unione Mat. Ital. (9) 2 (2009) 371-390 %G en_US %U http://hdl.handle.net/1963/2675 %1 1425 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-06-26T15:44:13Z\\nNo. of bitstreams: 1\\nDM-Gia-Pon.pdf: 242504 bytes, checksum: 3b08c25331a3436a5766d41df8e937f7 (MD5) %0 Journal Article %J Trans. Amer. Math. Soc. 361 (2009) 41-59 %D 2009 %T On viscosity solutions of Hamilton-Jacobi equations %A Sandro Zagatti %X We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions. %B Trans. Amer. Math. Soc. 361 (2009) 41-59 %I American Mathematical Society %G en_US %U http://hdl.handle.net/1963/3420 %1 915 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T11:15:26Z\\nNo. of bitstreams: 1\\nvisco1.pdf: 200249 bytes, checksum: d80a45752b5394539504d0029276b1dc (MD5) %R 10.1090/S0002-9947-08-04557-1 %0 Journal Article %J Arch. Ration. Mech. Anal. 189 (2008) 469-544 %D 2008 %T A vanishing viscosity approach to quasistatic evolution in plasticity with softening %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples. %B Arch. Ration. Mech. Anal. 189 (2008) 469-544 %G en_US %U http://hdl.handle.net/1963/1844 %1 2373 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-07-21T11:03:58Z\\nNo. of bitstreams: 1\\nmath.AP-0606718.pdf: 563956 bytes, checksum: 80e8ac8a9120c15b452698af3abc77d1 (MD5) %R 10.1007/s00205-008-0117-5 %0 Journal Article %J NATO Science for Peace and Security Series B: Physics and Biophysics %D 2008 %T Variational methods for Hamiltonian PDEs %A Massimiliano Berti %X We present recent existence results of periodic solutions for completely resonant nonlinear wave equations in which both "small divisor" difficulties and infinite dimensional bifurcation phenomena occur. These results can be seen as generalizations of the classical finite-dimensional resonant center theorems of Weinstein-Moser and Fadell-Rabinowitz. The proofs are based on variational bifurcation theory: after a Lyapunov-Schmidt reduction, the small divisor problem in the range equation is overcome with a Nash-Moser implicit function theorem for a Cantor set of non-resonant parameters. Next, the infinite dimensional bifurcation equation, variational in nature, possesses minimax mountain-pass critical points. The big difficulty is to ensure that they are not in the "Cantor gaps". This is proved under weak non-degeneracy conditions. Finally, we also discuss the existence of forced vibrations with rational frequency. This problem requires variational methods of a completely different nature, such as constrained minimization and a priori estimates derivable from variational inequalities. © 2008 Springer Science + Business Media B.V. %B NATO Science for Peace and Security Series B: Physics and Biophysics %P 391-420 %@ 9781402069628 %G eng %R 10.1007/978-1-4020-6964-2-16 %0 Journal Article %J J. Hyperbolic Differ. Equ. 4 (2007) 771-795 %D 2007 %T Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients %A Giuseppe Maria Coclite %A Nils Henrik Risebro %X We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions. %B J. Hyperbolic Differ. Equ. 4 (2007) 771-795 %I World Scientific %G en_US %U http://hdl.handle.net/1963/2907 %1 1793 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T10:55:33Z\\nNo. of bitstreams: 1\\nmath.AP0303288.pdf: 286583 bytes, checksum: ec274415af1f87dc1406bdc76cab8159 (MD5) %R 10.1142/S0219891607001355 %0 Journal Article %J Differential Geom. Appl. 24 (2006) 235-259 %D 2006 %T On variational approach to differential invariants of rank two distributions %A Igor Zelenko %X n the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his \\\"reduction-prolongation\\\" procedure. After Cartan\\\'s work the following questions remained open: first the geometric reason for existence of Cartan\\\'s tensor was not clear; secondly it was not clear how to generalize this tensor to other classes of distributions; finally there were no explicit formulas for computation of Cartan\\\'s tensor. Our paper is the first in the series of papers, where we develop an alternative approach, which gives the answers to the questions mentioned above. It is based on the investigation of dynamics of the field of so-called abnormal extremals (singular curves) of rank 2 distribution and on the general theory of unparametrized curves in the Lagrange Grassmannian, developed in our previous works with A. Agrachev . In this way we construct the fundamental form and the projective Ricci curvature of rank 2 vector distributions for arbitrary n greater than 4.\\nFor n=5 we give an explicit method for computation of these invariants and demonstrate it on several examples. In our next paper we show that in the case n=5 our fundamental form coincides with Cartan\\\'s tensor. %B Differential Geom. Appl. 24 (2006) 235-259 %G en_US %U http://hdl.handle.net/1963/2188 %1 2056 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T11:38:23Z\\nNo. of bitstreams: 1\\n0402171v2.pdf: 447361 bytes, checksum: e7f578202115704506587340079a39d3 (MD5) %R 10.1016/j.difgeo.2005.09.004 %0 Report %D 2006 %T Variational problems in fracture mechanics %A Gianni Dal Maso %X We present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of arbitrary space dimension with a general quasiconvex bulk energy and with prescribed boundary deformations and applied loads. %G en_US %U http://hdl.handle.net/1963/1816 %1 2398 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-18T12:50:25Z\\nNo. of bitstreams: 1\\nmath.AP0602614.pdf: 122115 bytes, checksum: 8a582db939c08c52510bcc1c7da7c563 (MD5) %0 Journal Article %J Ann. of Math. 161 (2005) 223-342 %D 2005 %T Vanishing viscosity solutions of nonlinear hyperbolic systems %A Stefano Bianchini %A Alberto Bressan %X We consider the Cauchy problem for a strictly hyperbolic, $n\\\\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation.\\nWe show that the solutions of the viscous approximations $u_t+A(u)u_x=\\\\ve u_{xx}$ are defined globally in time and satisfy uniform BV estimates, independent of $\\\\ve$. Moreover, they depend continuously on the initial data in the $\\\\L^1$ distance, with a Lipschitz constant independent of $t,\\\\ve$. Letting $\\\\ve\\\\to 0$, these viscous solutions converge to a unique limit, depending Lipschitz continuously on the initial data. In the conservative case where $A=Df$ is the Jacobian of some flux function $f:\\\\R^n\\\\mapsto\\\\R^n$, the vanishing viscosity limits are precisely the unique entropy weak solutions to the system of conservation laws $u_t+f(u)_x=0$. %B Ann. of Math. 161 (2005) 223-342 %I Annals of Mathematics %G en_US %U http://hdl.handle.net/1963/3074 %1 1259 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:46:16Z\\nNo. of bitstreams: 1\\n0111321v1.pdf: 746310 bytes, checksum: f3b7c9e76e33050e9f367ba2c57e2161 (MD5) %0 Journal Article %J Comm. Math.\\nPhys. 250 (2004) 161-193. %D 2004 %T Virasoro Symmetries of the Extended Toda Hierarchy %A Boris Dubrovin %A Zhang Youjin %X We prove that the extended Toda hierarchy of \\\\cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_m$, $m\\\\geq -1$ of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination of the Virasoro operators and the flows of the hierarchy. As an application we show that the validity of the Virasoro constraints for the $CP^1$ Gromov-Witten invariants and their descendents implies that their generating function is the logarithm of a particular tau function of the extended Toda hierarchy. %B Comm. Math.\\nPhys. 250 (2004) 161-193. %G en_US %U http://hdl.handle.net/1963/2544 %1 1575 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T12:53:52Z\\nNo. of bitstreams: 1\\n0308152v2.pdf: 341202 bytes, checksum: 306b1f696e6ec01c0eabbeeeca895290 (MD5) %R 10.1007/s00220-004-1084-9 %0 Journal Article %J ESAIM Control Optim. Calc. Var., 5 (2000), n. 5, p. 369-393. %D 2000 %T Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities %A Gianni Dal Maso %A Helene Frankowska %B ESAIM Control Optim. Calc. Var., 5 (2000), n. 5, p. 369-393. %I SISSA Library %G en %U http://hdl.handle.net/1963/1514 %1 2649 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:28Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0006013.pdf: 255518 bytes, checksum: 30b8f57e76e4104aa6c3efc013b76620 (MD5)\\r\\n Previous issue date: 2000 %R 10.1051/cocv:2000114 %0 Journal Article %D 1999 %T Vanishing viscosity solutions of hyperbolic systems on manifolds %A Stefano Bianchini %A Alberto Bressan %I SISSA Library %G en %U http://hdl.handle.net/1963/1238 %1 2705 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:09Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 %D 1999 %T Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case %A Andrea Braides %A Gianni Dal Maso %A Adriana Garroni %X Starting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included. %B Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 %I Springer %G en_US %U http://hdl.handle.net/1963/3371 %1 959 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-28T17:18:31Z\\nNo. of bitstreams: 1\\nVariational_formulation.pdf: 2100868 bytes, checksum: 88bfc4cfb6072391f1c6d7cd06e7b8ec (MD5) %R 10.1007/s002050050135 %0 Journal Article %J J. Math. Anal. Appl. 232 (1999) 1-19 %D 1999 %T The vector measures whose range is strictly convex %A Stefano Bianchini %A Carlo Mariconda %B J. Math. Anal. Appl. 232 (1999) 1-19 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3546 %1 1155 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-25T09:57:33Z\\nNo. of bitstreams: 1\\nvectormeasures.pdf: 229747 bytes, checksum: 57a43435ba8fcbc2831435e629e80f7a (MD5) %R 10.1006/jmaa.1998.6215 %0 Journal Article %J Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 %D 1997 %T Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws %A Graziano Crasta %A Benedetto Piccoli %B Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 %I SISSA Library %G en %U http://hdl.handle.net/1963/969 %1 3485 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J SIAM J. Control Optim. 32 (1994) 1114-1127 %D 1994 %T A version of Olech\\\'s lemma in a problem of the calculus of variations %A Arrigo Cellina %A Sandro Zagatti %X This paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data. %B SIAM J. Control Optim. 32 (1994) 1114-1127 %I SIAM %G en_US %U http://hdl.handle.net/1963/3514 %1 750 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-12T14:59:35Z\\nNo. of bitstreams: 1\\ncellina.pdf: 1532989 bytes, checksum: a1e477c545eaaf66420216c3e5c4c153 (MD5) %R 10.1137/S0363012992234669 %0 Journal Article %J Acta Math. 168 (1992), no.1-2, p. 89-151 %D 1992 %T A variational method in image segmentation: existence and approximation result %A Gianni Dal Maso %A Jean-Michel Morel %A Sergio Solimini %B Acta Math. 168 (1992), no.1-2, p. 89-151 %I SISSA Library %G en %U http://hdl.handle.net/1963/808 %1 2983 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:13Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989) %D 1988 %T Variational inequalities for the biharmonic operator with variable obstacles. %A Gianni Dal Maso %A Gabriella Paderni %B Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989) %I SISSA Library %G en %U http://hdl.handle.net/1963/531 %1 3373 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:03Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Thesis %D 1988 %T Variational Problems with Obstructions %A Roberta Musina %I SISSA %G en %U http://hdl.handle.net/1963/5832 %1 5683 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-15T10:46:56Z\\nNo. of bitstreams: 1\\nPhD_Musina_Roberta.pdf: 10260545 bytes, checksum: 5aebbcbae10f3a5388571a5a85abc8bd (MD5)