We study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

%B Advances in Calculus of Variations %I De Gruyter %V 10 %P 183–207 %G eng %R 10.1515/acv-2015-0036 %0 Journal Article %J Journal de Mathématiques Pures et Appliquées %D 2017 %T A lower semicontinuity result for a free discontinuity functional with a boundary term %A Stefano Almi %A Gianni Dal Maso %A Rodica Toader %XWe study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

%B Journal de Mathématiques Pures et Appliquées %V 108 %P 952-990 %G en %U http://hdl.handle.net/20.500.11767/15979 %N 6 %1 34731 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2015-12-15T14:37:19Z No. of bitstreams: 1 Alm-DM-Toa-15-sissa.pdf: 351559 bytes, checksum: b6adddc4944478676c7d4b34028a347c (MD5) %& 952 %R 10.1016/j.matpur.2017.05.018 %0 Journal Article %J Journal of Differential Equations %D 2016 %T Existence and uniqueness of dynamic evolutions for a peeling test in dimension one %A Gianni Dal Maso %A Giuliano Lazzaroni %A Lorenzo Nardini %K Dynamic debonding %K Dynamic energy release rate %K Dynamic fracture %K Griffith's criterion %K Maximum dissipation principle %K Wave equation in time-dependent domains %XIn this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

%B Journal of Differential Equations %V 261 %P 4897 - 4923 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039616301772 %R https://doi.org/10.1016/j.jde.2016.07.012 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2016 %T Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %XWe study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

%B Calculus of Variations and Partial Differential Equations %V 55 %P 45 %8 Apr %G eng %U https://doi.org/10.1007/s00526-016-0981-z %R 10.1007/s00526-016-0981-z %0 Report %D 2016 %T A model for the quasistatic growth of cracks with fractional dimension %A Gianni Dal Maso %A Marco Morandotti %X We study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated. %G en %U http://urania.sissa.it/xmlui/handle/1963/35175 %1 35459 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-03-01T11:58:09Z No. of bitstreams: 1 DM-Mor-15-SISSA.pdf: 333769 bytes, checksum: f89da17dcba29091a91c253127244ede (MD5) %0 Report %D 2015 %T Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X There are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions. %G en %U http://urania.sissa.it/xmlui/handle/1963/35045 %1 35277 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2015-11-18T15:46:32Z No. of bitstreams: 1 DM-Lar-Toa-SISSA.pdf: 313034 bytes, checksum: 76419fd2c8c435ae7deeca773b424667 (MD5) %0 Report %D 2015 %T The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data %A Gianni Dal Maso %A Ilaria Lucardesi %X Given a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks. %G en %U http://urania.sissa.it/xmlui/handle/1963/34629 %1 34832 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by lucardes@sissa.it (lucardes@sissa.it) on 2015-10-12T09:08:37Z No. of bitstreams: 1 DM-Luc-15-SISSA.pdf: 376913 bytes, checksum: bfdcf0975c25c9366acb4195e0f08e79 (MD5) %0 Journal Article %D 2014 %T Editorial %A Ciro Ciliberto %A Gianni Dal Maso %A Pasquale Vetro %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34712 %1 34926 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T10:50:12Z (GMT) No. of bitstreams: 0 %R 10.1007/s12215-014-0172-8 %0 Journal Article %D 2014 %T Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length %A Gianni Dal Maso %A Gianluca Orlando %A Rodica Toader %K cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions %XWe consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

%I SISSA %G en %U http://hdl.handle.net/1963/7271 %1 7316 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-03-11T15:17:50Z No. of bitstreams: 1 DM-Orl-Toa-sissa.pdf: 251851 bytes, checksum: 59273a217a11dcfc5a9ed89d2c34c6cd (MD5) %R 10.1007/s00030-014-0291-0 %0 Journal Article %D 2014 %T New results on Gamma-limits of integral functionals %A Nadia Ansini %A Gianni Dal Maso %A Caterina Ida Zeppieri %K Gamma-convergence %I Elsevier %G en %U http://hdl.handle.net/1963/5880 %1 5745 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T12:48:08Z No. of bitstreams: 1 03M_2012_Ansini.pdf: 262251 bytes, checksum: 4e0dd5c07ab75bd2da8aa462f2ae8f0f (MD5) %R 10.1016/j.anihpc.2013.02.005 %0 Journal Article %J Nonlinear Analysis %D 2014 %T Quasi-static crack growth in hydraulic fracture %A Stefano Almi %A Gianni Dal Maso %A Rodica Toader %XWe present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

%B Nonlinear Analysis %I Elsevier %V 109 %P 301-318 %G en %U http://hdl.handle.net/20.500.11767/17350 %N Nov %9 Journal article %1 34741 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by salmi@sissa.it (salmi@sissa.it) on 2015-09-24T08:10:23Z No. of bitstreams: 1 A-DM-T-070714.pdf: 283645 bytes, checksum: 68056ef27e9dcfa246029148c0016c0f (MD5) %& 301 %R 10.1016/j.na.2014.07.009 %0 Journal Article %J Journal of Dynamics and Differential Equations %D 2014 %T Quasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes %A Gianni Dal Maso %A Riccardo Scala %XWe introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

%B Journal of Dynamics and Differential Equations %V 26 %P 915–954 %8 Dec %G eng %U https://doi.org/10.1007/s10884-014-9409-7 %R 10.1007/s10884-014-9409-7 %0 Journal Article %D 2014 %T Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K Gamma-convergence, Cahn-Hilliard functional, phase transitions %X The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values. %I SISSA %G en %U http://hdl.handle.net/1963/7390 %1 7439 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-06-19T16:24:43Z No. of bitstreams: 1 DM-Fon-Leo-14-sissa.pdf: 409621 bytes, checksum: 40ba0baf0686b18dcd89582772f376b5 (MD5) %0 Journal Article %D 2013 %T Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K singular nonlinear parabolic equations, Hilbert transform, thin films %X In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6]. %I Springer %G en %U http://hdl.handle.net/1963/7245 %1 7284 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-01-15T08:47:14Z No. of bitstreams: 1 DM-Fon-Leo.pdf: 409459 bytes, checksum: 07429e936667a481a2c093217e585e84 (MD5) %R 10.1007/s00205-014-0730-4 %0 Report %D 2013 %T Attainment results for nematic elastomers %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %X We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids. %I SISSA %G en %U http://hdl.handle.net/1963/7174 %1 7201 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-10-22T14:32:26Z No. of bitstreams: 1 Ago-DM-DeS-13-sissa.pdf: 394672 bytes, checksum: d02690a6c7f206310d28d253ce53d0d3 (MD5) %0 Journal Article %J Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %D 2013 %T Fracture models as Gamma-limits of damage models %A Gianni Dal Maso %A Flaviana Iurlano %XWe analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

%B Communications on Pure and Applied Analysis 12 (2013) 1657-1686 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/4225 %1 3952 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-23T11:09:07Z\\r\\nNo. of bitstreams: 1\\r\\nDalMaso_Iurlano_25_M.pdf: 360594 bytes, checksum: a0e0909b1c483748ede26b7e785a1d79 (MD5) %R 10.3934/cpaa.2013.12.1657 %0 Journal Article %D 2013 %T One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls %A Gianni Dal Maso %A Antonio DeSimone %A Marco Morandotti %XIn this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

%I SISSA %G en %U http://hdl.handle.net/1963/6467 %1 6412 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-02-11T12:13:39Z No. of bitstreams: 1 DM-DeS-Mor-12-v10 sissa.pdf: 606490 bytes, checksum: 45f448186465b198ec31beb54afb0edf (MD5) %0 Journal Article %J Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 %D 2012 %T Gamma-convergence and H-convergence of linear elliptic operators %A Nadia Ansini %A Gianni Dal Maso %A Caterina Ida Zeppieri %K Linear elliptic operators %B Journal de Mathématiques Pures et Appliquées, Available online 12 September 2012 %I Elsevier %G en %U http://hdl.handle.net/1963/5878 %1 5746 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T13:02:32Z\\r\\nNo. of bitstreams: 1\\r\\n04M_2012_Ansini.pdf: 226441 bytes, checksum: 789582b685e552b522a3e8a896e091f8 (MD5) %R 10.1016/j.matpur.2012.09.004 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire %D 2012 %T Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %K Nonlinear elasticity %XThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

%B Ann. Inst. H. Poincare Anal. Non Lineaire %I Gauthier-Villars;Elsevier %V 29 %P 715-735 %G en %U http://hdl.handle.net/1963/4267 %1 3996 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T15:11:45Z\\r\\nNo. of bitstreams: 1\\r\\nAgostiniani_DalMaso_30_M.pdf: 407057 bytes, checksum: 2009d1218f7735191a1c768a73b400a3 (MD5) %R 10.1016/j.anihpc.2012.04.001 %0 Journal Article %J Calculus of variations and partial differential equations 44 (2012) 495-541 %D 2012 %T Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution %A Gianni Dal Maso %A Antonio DeSimone %A Francesco Solombrino %XCam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

%B Calculus of variations and partial differential equations 44 (2012) 495-541 %I Springer %G en_US %U http://hdl.handle.net/1963/3900 %1 809 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-26T09:17:50Z\\r\\nNo. of bitstreams: 1\\r\\nSolombrino_46M.pdf: 382911 bytes, checksum: dd118cc7f80d4cb1902713eb18747ac6 (MD5) %R 10.1007/s00526-011-0443-6 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 %D 2011 %T Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem %A Gianni Dal Maso %A Giuliano Lazzaroni %X We present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3801 %1 526 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-27T10:24:55Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Laz-proc-pre.pdf: 195002 bytes, checksum: 44e408b134f19e4d31e77b3e0762cd73 (MD5) %R 10.3934/dcds.2011.31.1219 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %D 2011 %T Ennio De Giorgi and Γ-convergence %A Gianni Dal Maso %X Γ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/5308 %1 5138 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-31T12:04:34Z\\nNo. of bitstreams: 0 %R 10.3934/dcds.2011.31.1017 %0 Journal Article %J SIAM J. Math. Anal. %D 2011 %T An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers %A Gianni Dal Maso %A Antonio DeSimone %A Marco Morandotti %XWe present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

%B SIAM J. Math. Anal. %I Society for Industrial and Applied Mathematics %V 43 %P 1345-1368 %G en_US %U http://hdl.handle.net/1963/3894 %1 815 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T11:44:06Z\\r\\nNo. of bitstreams: 1\\r\\nMorandotti_44M.pdf: 217358 bytes, checksum: 4c362016bb2220e7a97805254b7fb870 (MD5) %R 10.1137/10080083X %0 Journal Article %J Rend. Lincei Mat. Appl. 22 (2011) 387-408 %D 2011 %T Existence for wave equations on domains with arbitrary growing cracks %A Gianni Dal Maso %A Cristopher J. Larsen %K Wave equation %X In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation. %B Rend. Lincei Mat. Appl. 22 (2011) 387-408 %I European Mathematical Society %G en %U http://hdl.handle.net/1963/4284 %1 4015 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-27T09:09:30Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Lar_32_M.pdf: 223891 bytes, checksum: 7c6c66b6d21936b33ed0c21574928e24 (MD5) %R 10.4171/RLM/606 %0 Journal Article %J J. Eur. Math. Soc. (JEMS), to appear %D 2011 %T Generalised functions of bounded deformation %A Gianni Dal Maso %K free discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability %XWe introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

%B J. Eur. Math. Soc. (JEMS), to appear %I SISSA %G en %U http://hdl.handle.net/1963/6374 %1 6309 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-10T18:54:48Z\\nNo. of bitstreams: 1\\nDM-11.pdf: 413971 bytes, checksum: eca2a953ba1b97755da281bca4e099e4 (MD5) %0 Journal Article %J Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 %D 2011 %T Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling %A Gianni Dal Maso %A Antonio DeSimone %A Francesco Solombrino %K Cam-Clay plasticity %XCam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

%B Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 %I Springer %G en_US %U http://hdl.handle.net/1963/3670 %1 635 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-20T08:26:03Z\\r\\nNo. of bitstreams: 1\\r\\nDM-DeS-Sol-36_2009_preprint.pdf: 421582 bytes, checksum: 011806364200378d6deec80b88978550 (MD5) %R 10.1007/s00526-010-0336-0 %0 Journal Article %J Indiana Univ. Math. J. 60 (2011) 367-409 %D 2011 %T Singular perturbation models in phase transitions for second order materials %A Milena Chermisi %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %X A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained. %B Indiana Univ. Math. J. 60 (2011) 367-409 %I Indiana University %G en_US %U http://hdl.handle.net/1963/3858 %1 851 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:47:12Z\\r\\nNo. of bitstreams: 1\\r\\nCheDMaFonLeo_2010.pdf: 350746 bytes, checksum: b384a4d0b82dd9713e1849ad3ef6a2be (MD5) %R 10.1512/iumj.2011.60.4346 %0 Journal Article %J Adv. Calc. Var. 3 (2010) 345-370 %D 2010 %T Homogenization of fiber reinforced brittle material: the intermediate case %A Gianni Dal Maso %A Caterina Ida Zeppieri %X We derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure. %B Adv. Calc. Var. 3 (2010) 345-370 %I Walter de Gruyter %G en_US %U http://hdl.handle.net/1963/3607 %1 694 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-02T10:43:00Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Zep.pdf: 294507 bytes, checksum: 5ba95ca12abb15953a564aeedf353087 (MD5) %R 10.1515/ACV.2010.011 %0 Journal Article %J Adv. Calc. Var. 3 (2010) 287-319 %D 2010 %T Nonlocal character of the reduced theory of thin films with higher order perturbations %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %B Adv. Calc. Var. 3 (2010) 287-319 %G en_US %U http://hdl.handle.net/1963/3754 %1 563 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-09-15T09:06:42Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo.pdf: 288658 bytes, checksum: 7815e9376b53eb044b2fb2b57cd49b53 (MD5) %R 10.1515/ACV.2010.012, /July/2010 %0 Journal Article %J Arch. Ration. Mech. Anal. 196 (2010) 867-906 %D 2010 %T Quasistatic crack growth in elasto-plastic materials: the two-dimensional case %A Gianni Dal Maso %A Rodica Toader %X We study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity. %B Arch. Ration. Mech. Anal. 196 (2010) 867-906 %G en_US %U http://hdl.handle.net/1963/2964 %1 1736 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-23T17:17:34Z\\nNo. of bitstreams: 1\\nDM-Toa-07-preprint.pdf: 320979 bytes, checksum: e4f2a1856f9bd91d63fc45557cbd6a16 (MD5) %R 10.1007/s00205-009-0258-1 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290 %D 2010 %T Quasistatic crack growth in finite elasticity with non-interpenetration %A Gianni Dal Maso %A Giuliano Lazzaroni %XWe present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

%B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290 %G en_US %U http://hdl.handle.net/1963/3397 %1 935 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-15T09:16:46Z\\nNo. of bitstreams: 1\\nDM-Laz-08pre.pdf: 360778 bytes, checksum: 14a35b4647fde0ea0931df8ae6cbfb73 (MD5) %R 10.1016/j.anihpc.2009.09.006 %0 Journal Article %J Netw. Heterog. Media 5 (2010) 97-132 %D 2010 %T Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case %A Gianni Dal Maso %A Francesco Solombrino %K Cam-Clay plasticity %XWe study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.

%B Netw. Heterog. Media 5 (2010) 97-132 %G en_US %U http://hdl.handle.net/1963/3671 %1 634 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-20T08:35:17Z\\nNo. of bitstreams: 1\\nDM-Sol2-39_2009_preprint.pdf: 345995 bytes, checksum: 073ce622e3320be1f56a1cc9f8904fae (MD5) %R 10.3934/nhm.2010.5.97 %0 Journal Article %J SIAM J. Math. Anal. 40 (2009) 2351-2391 %D 2009 %T A higher order model for image restoration: the one dimensional case %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %A Massimiliano Morini %X The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals. %B SIAM J. Math. Anal. 40 (2009) 2351-2391 %G en_US %U http://hdl.handle.net/1963/3174 %1 1127 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-23T07:52:52Z\\nNo. of bitstreams: 1\\nDM-Fon-Leo-Mor-08-preprint.pdf: 336946 bytes, checksum: 32db893a2b928f559b6744296e1d4f2c (MD5) %R 10.1137/070697823 %0 Journal Article %J SIAM J. Math. Anal. 41 (2009) 1874-1889 %D 2009 %T Homogenization of fiber reinforced brittle materials: the extremal cases %A Marco Barchiesi %A Gianni Dal Maso %X We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively. %B SIAM J. Math. Anal. 41 (2009) 1874-1889 %I SIAM %G en_US %U http://hdl.handle.net/1963/2705 %1 1396 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-13T12:57:01Z\\nNo. of bitstreams: 1\\nmicrofibre.pdf: 236545 bytes, checksum: 53ef9ce789d27bba7dcac550930f306b (MD5) %0 Journal Article %J Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 %D 2009 %T Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions %A Gianni Dal Maso %A Antonio DeSimone %X We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation. %B Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 %G en_US %U http://hdl.handle.net/1963/3395 %1 937 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-10T11:56:05Z\\nNo. of bitstreams: 1\\nDal_Maso-DeSimone.pdf: 1160572 bytes, checksum: fd49c80a369183f1941b0fcf3cd65341 (MD5) %R 10.1142/S0218202509003942 %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 Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %D 2008 %T Decomposition results for functions with bounded variation %A Gianni Dal Maso %A Rodica Toader %B Boll. Unione Mat. Ital. (9) 1 (2008) 497-505 %I Unione Matematica Italiana %G en_US %U http://hdl.handle.net/1963/3535 %1 729 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T10:23:36Z\\nNo. of bitstreams: 1\\nDM-Toa.pdf: 186814 bytes, checksum: bbc754f60013f0d8fd61b90a278ac837 (MD5) %0 Journal Article %J Netw. Heterog. Media 3 (2008) 567-614 %D 2008 %T Globally stable quasistatic evolution in plasticity with softening %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response. %B Netw. Heterog. Media 3 (2008) 567-614 %G en_US %U http://hdl.handle.net/1963/1965 %1 2228 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-05-15T11:03:21Z\\nNo. of bitstreams: 1\\nDM-DeS-Mor-Mor-05-3-final.pdf: 395475 bytes, checksum: 5789494df44986207d416d5d1ea15d22 (MD5) %0 Journal Article %J Calc. Var. Partial Differential Equations 31 (2008) 137-145 %D 2008 %T Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics %A Gianni Dal Maso %A Adriana Garroni %X In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem. %B Calc. Var. Partial Differential Equations 31 (2008) 137-145 %G en_US %U http://hdl.handle.net/1963/1723 %1 2428 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-26T12:52:13Z\\nNo. of bitstreams: 1\\nmath.AP0507088.pdf: 132125 bytes, checksum: 444c743b7852d0f6e97bb318f49b4467 (MD5) %R 10.1007/s00526-006-0084-3 %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 NoDEA 13 (2007) 713-734 %D 2007 %T On a notion of unilateral slope for the Mumford-Shah functional %A Gianni Dal Maso %A Rodica Toader %X In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional. %B NoDEA 13 (2007) 713-734 %G en_US %U http://hdl.handle.net/1963/2059 %1 2137 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-06T14:02:51Z\\nNo. of bitstreams: 1\\n0410525v1.pdf: 214576 bytes, checksum: 3722f413401cdb51f778a8c15eeebe71 (MD5) %R 10.1007/s00030-006-4054-4 %0 Report %D 2007 %T Quasistatic crack growth for a cohesive zone model with prescribed crack path %A Gianni Dal Maso %A Chiara Zanini %X In this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes. %B Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253-279 %G en_US %U http://hdl.handle.net/1963/1686 %1 2447 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-06-20T12:05:32Z\\nNo. of bitstreams: 1\\nDM-Zan-04.pdf: 312529 bytes, checksum: 2373a684663d7901c85daad77c7aa8b6 (MD5) %R 10.1017/S030821050500079X %0 Journal Article %J Milan J. Math. 75 (2007) 117-134 %D 2007 %T Quasistatic evolution problems for pressure-sensitive plastic materials %A Gianni Dal Maso %A Alexey Demyanov %A Antonio DeSimone %X We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity. %B Milan J. Math. 75 (2007) 117-134 %G en_US %U http://hdl.handle.net/1963/1962 %1 2231 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-05-15T10:32:12Z\\nNo. of bitstreams: 1\\nSissa27_2007M.pdf: 223083 bytes, checksum: a4cdbb7a1018403355c560749680e47a (MD5) %R 10.1007/s00032-007-0071-y %0 Report %D 2007 %T Time-dependent systems of generalized Young measures %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %A Massimiliano Morini %X In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time. %B Netw. Heterog. Media 2 (2007) 1-36 %G en_US %U http://hdl.handle.net/1963/1795 %1 2749 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-04T13:16:42Z\\nNo. of bitstreams: 1\\n98M-2005.pdf: 339547 bytes, checksum: 695874ce74733dc0020a7e357f04cb1b (MD5) %0 Journal Article %J Arch. Ration. Mech. Anal. 180 (2006) 237-291 %D 2006 %T Quasistatic evolution problems for linearly elastic-perfectly plastic materials %A Gianni Dal Maso %A Antonio DeSimone %A Maria Giovanna Mora %X The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain. %B Arch. Ration. Mech. Anal. 180 (2006) 237-291 %G en_US %U http://hdl.handle.net/1963/2129 %1 2114 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T10:14:12Z\\nNo. of bitstreams: 1\\n0412212v1.pdf: 419970 bytes, checksum: fa4e3c2a5db22bfa28aa4f682cb55da4 (MD5) %R 10.1007/s00205-005-0407-0 %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 Arch. Ration. Mech. Anal. 176 (2005) 165-225 %D 2005 %T Quasistatic Crack Growth in Nonlinear Elasticity %A Gianni Dal Maso %A Gilles A. Francfort %A Rodica Toader %X In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time. %B Arch. Ration. Mech. Anal. 176 (2005) 165-225 %G en_US %U http://hdl.handle.net/1963/2293 %1 1723 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-24T09:12:09Z\\nNo. of bitstreams: 1\\n0401196v1.pdf: 664295 bytes, checksum: cb1000c44e6ae356984e24b55ee97117 (MD5) %R 10.1007/s00205-004-0351-4 %0 Generic %D 2005 %T Solutions of Neumann problems in domains with cracks and applications to fracture mechanics %A Gianni Dal Maso %G en_US %U http://hdl.handle.net/1963/1684 %1 79 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2005-05-20T07:18:38Z\\nNo. of bitstreams: 1\\nmath.AP0105132.pdf: 225826 bytes, checksum: d7308b70020a416522235ed54b404379 (MD5) %0 Journal Article %J Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %D 2004 %T Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains %A Gianni Dal Maso %A Francois Murat %X We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains. %B Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %I SISSA Library %G en %U http://hdl.handle.net/1963/1611 %1 2507 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:17Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0205225.pdf: 404809 bytes, checksum: 472524cb28afed2e55fcf0a7c46e7598 (MD5)\\r\\n Previous issue date: 2002 %0 Journal Article %J Arch. Ration. Mech. Anal. 171 (2004) 55-81 %D 2004 %T Higher order quasiconvexity reduces to quasiconvexity %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %A Massimiliano Morini %X In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems. %B Arch. Ration. Mech. Anal. 171 (2004) 55-81 %I Springer %G en_US %U http://hdl.handle.net/1963/2911 %1 1789 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:36:19Z\\nNo. of bitstreams: 1\\nmath.AP0305138.pdf: 272082 bytes, checksum: 245f93702444ac3eb1de7c86c1f83551 (MD5) %R 10.1007/s00205-003-0278-1 %0 Journal Article %J Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 %D 2004 %T Quasi-static evolution in brittle fracture: the case of bounded solutions %A Gianni Dal Maso %A Gilles A. Francfort %A Rodica Toader %X The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$. %B Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266 %G en_US %U http://hdl.handle.net/1963/2229 %1 2015 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T15:04:28Z\\r\\nNo. of bitstreams: 1\\r\\n0401198v1.pdf: 166634 bytes, checksum: c21fba2b1fbbaec4fe14c56595b0664e (MD5) %0 Journal Article %J Applied Math.Optim. 48 (2003), no.1, p.39-66 %D 2003 %T Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations %A Gianni Dal Maso %A Helene Frankowska %B Applied Math.Optim. 48 (2003), no.1, p.39-66 %I SISSA Library %G en %U http://hdl.handle.net/1963/1625 %1 2493 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:30Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207230.pdf: 302400 bytes, checksum: e660ec855386e1a29edd2e20f7abc796 (MD5)\\r\\n Previous issue date: 2002 %R 10.1007/s00245-003-0768-4 %0 Journal Article %J Calc. Var. Partial Differential Equations 16 (2003) 299-333 %D 2003 %T The calibration method for the Mumford-Shah functional and free-discontinuity problems %A Giovanni Alberti %A Guy Bouchitte %A Gianni Dal Maso %X We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results. %B Calc. Var. Partial Differential Equations 16 (2003) 299-333 %I Springer %G en_US %U http://hdl.handle.net/1963/3051 %1 1282 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:00:19Z\\nNo. of bitstreams: 1\\n0105013v1.pdf: 428802 bytes, checksum: de75d15134f2a74b36b0d71355e04835 (MD5) %R 10.1007/s005260100152 %0 Journal Article %J J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 %D 2003 %T A stability result for nonlinear Neumann problems under boundary variations %A Gianni Dal Maso %A Francois Ebobisse %A Marcello Ponsiglione %X In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology. %B J.Math. Pures Appl. (9) 82 (2003) no.5 , 503 %I SISSA Library %G en %U http://hdl.handle.net/1963/1618 %1 2500 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:23Z (GMT). No. of bitstreams: 1\\nmath.AP0206215.pdf: 329673 bytes, checksum: 40d537fd197fbaec56be0729d3a72ee3 (MD5)\\n Previous issue date: 2002 %R 10.1016/S0021-7824(03)00014-X %0 Journal Article %J Set-Valued Anal. 10 (2002), p.165-183 %D 2002 %T Linearized elasticity as gamma-limit of finite elasticity %A Gianni Dal Maso %A Matteo Negri %A Danilo Percivale %B Set-Valued Anal. 10 (2002), p.165-183 %I Springer %G en_US %U http://hdl.handle.net/1963/3052 %1 1281 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:20:52Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Neg-Per-01.pdf: 199909 bytes, checksum: ddd0bf6c6890234f6d9c820fd6ab7f47 (MD5) %R 10.1023/A:1016577431636 %0 Journal Article %J Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 %D 2002 %T A model for the quasi-static growth of a brittle fracture: existence and approximation results %A Gianni Dal Maso %A Rodica Toader %X We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough. %B Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773 %I SISSA Library %G en %U http://hdl.handle.net/1963/1571 %1 2547 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:18Z (GMT). No. of bitstreams: 1\\nmath.AP0101089.pdf: 313965 bytes, checksum: 0373da7254cb4d172659dd2402174562 (MD5)\\n Previous issue date: 2000 %R 10.1142/S0218202502002331 %0 Journal Article %J Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. %D 2002 %T A model for the quasi-static growth of brittle fractures based on local minimization %A Gianni Dal Maso %A Rodica Toader %X We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith\\\'s criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough. %B Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800. %I SISSA Library %G en %U http://hdl.handle.net/1963/1621 %1 2497 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:26Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207002.pdf: 268810 bytes, checksum: 00401d0491ec9d938b05dcdb884832b7 (MD5)\\r\\n Previous issue date: 2002 %R 10.1142/S0218202502002331 %0 Journal Article %J Arch. Ration. Mech. Anal. 162 (2002) 101-135 %D 2002 %T A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results %A Gianni Dal Maso %A Rodica Toader %X We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith\\\'s theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although we can not exclude that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the continuous time evolution. %B Arch. Ration. Mech. Anal. 162 (2002) 101-135 %I Springer %G en_US %U http://hdl.handle.net/1963/3056 %1 1277 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T16:01:33Z\\nNo. of bitstreams: 1\\n0103221v1.pdf: 340988 bytes, checksum: 433e8545f072a326fc7a6d80a9e7a401 (MD5) %R 10.1007/s002050100187 %0 Journal Article %J Acta Appl. Math., 2001, 65, 207-215 %D 2001 %T Gamma-limit of periodic obstacles %A Gianni Dal Maso %A Paola Trebeschi %X We compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles. %B Acta Appl. Math., 2001, 65, 207-215 %I SISSA Library %G en %U http://hdl.handle.net/1963/1495 %1 2668 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:12Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1010668530972 %0 Journal Article %J Adv. Math. Sci. Appl. 11 (2001) 721-751 %D 2001 %T A monotonicity approach to nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %X We study the asymptotic behaviour of solutions to Dirichlet problems in perforated domains for nonlinear elliptic equations associated with monotone operators. The main difference with respect to the previous papers on this subject is that no uniformity is assumed in the monotonicity condition. Under a very general hypothesis on the holes of the domains, we construct a limit equation, which is satisfied by the weak limits of the solutions. The additional term in the limit problem depends only on the local behaviour of the holes, which can be expressed in terms of suitable nonlinear capacities associated with the monotone operator. %B Adv. Math. Sci. Appl. 11 (2001) 721-751 %I SISSA Library %G en %U http://hdl.handle.net/1963/1555 %1 2563 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:04:04Z (GMT). No. of bitstreams: 1\\nmath.AP0010232.pdf: 246554 bytes, checksum: 691b6fb5c795a48324b128ced5a3cc44 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J Optimal control and partial differential equations : in honour of professor Alain Bensoussan\\\'s 60th birthday / edited by José Luis Menaldi, Edmundo Rofman, and Agnès Sulem.,Amsterdam : IOS Press, 2001, p. 335-345 %D 2001 %T Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations %A Gianni Dal Maso %A Helene Frankowska %X We prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of solution, where classical derivatives are replaced only by subdifferentials. These results follow from a new comparison theorem for lower semicontinuous viscosity supersolutions of the Hamilton-Jacobi equation, that is proved in the general case of lower semicontinuous Lagrangians. %B Optimal control and partial differential equations : in honour of professor Alain Bensoussan\\\'s 60th birthday / edited by José Luis Menaldi, Edmundo Rofman, and Agnès Sulem.,Amsterdam : IOS Press, 2001, p. 335-345 %I SISSA Library %G en %U http://hdl.handle.net/1963/1515 %1 2648 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:29Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0006015.pdf: 143977 bytes, checksum: 23794ed600a1b20f94c6b1eca86fcc54 (MD5)\\r\\n Previous issue date: 2000 %0 Journal Article %J European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326. %D 2000 %T The Calibration Method for Free Discontinuity Problems %A Gianni Dal Maso %X The calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems. %B European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326. %I SISSA Library %G en %U http://hdl.handle.net/1963/1496 %1 2667 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:13Z (GMT). No. of bitstreams: 1\\r\\nmath.OC0006016.pdf: 150581 bytes, checksum: dde42438e52ad82f5980d68f697f90c8 (MD5)\\r\\n Previous issue date: 2000 %0 Journal Article %J J. Math. Pures Appl. 79, 2 (2000) 141-162 %D 2000 %T Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets %A Gianni Dal Maso %A Maria Giovanna Mora %A Massimiliano Morini %B J. Math. Pures Appl. 79, 2 (2000) 141-162 %I SISSA Library %G en %U http://hdl.handle.net/1963/1261 %1 3194 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:27Z (GMT). No. of bitstreams: 1\\nmath-FA0006073.pdf: 195688 bytes, checksum: 199483eeec8fa727b6f84ce5270d3f32 (MD5)\\n Previous issue date: 1999 %R 10.1016/S0021-7824(99)00140-3 %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 %J Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %D 1999 %T Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %@ 1618-1891 %G en %U http://hdl.handle.net/1963/6433 %1 6374 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:25:49Z\\nNo. of bitstreams: 0 %R 10.1007/BF01759365 %0 Journal Article %J C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 %D 1999 %T The calibration method for the Mumford-Shah functional %A Giovanni Alberti %A Guy Bouchitte %A Gianni Dal Maso %X In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3). %B C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 %I Elsevier %G en %U http://hdl.handle.net/1963/1235 %1 2708 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:07Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0764-4442(00)88602-4 %0 Journal Article %J M2AN 33 (1999) 651-672 %D 1999 %T Discrete approximation of the Mumford-Shah functional in dimension two %A Antonin Chambolle %A Gianni Dal Maso %B M2AN 33 (1999) 651-672 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/3588 %1 712 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T13:50:04Z\\nNo. of bitstreams: 1\\nDalMaso1999.pdf: 462659 bytes, checksum: 04dc23ba4544d5be9ebdd703da477c7e (MD5) %R 10.1051/m2an:1999156 %0 Journal Article %J Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 %D 1999 %T Evans-Vasilesco theorem in Dirichlet spaces %A Gianni Dal Maso %A Virginia De Cicco %B Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 %I SISSA %G en %U http://hdl.handle.net/1963/6436 %1 6376 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:39:11Z\\nNo. of bitstreams: 2\\nDM-DeC-96.pdf: 145467 bytes, checksum: 0cf974ac5cc090ff7f9faae3d433043f (MD5)\\nDM-DeC-96-cover.pdf: 35849 bytes, checksum: cde85af897042e1ee2c1b1a8c724b8eb (MD5) %0 Journal Article %J Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717 %D 1999 %T A Lipschitz selection from the set of minimizers of a nonconvex functional of the gradient %A Gianni Dal Maso %A Vladimir V. Goncharov %A Antonio Ornelas %X A constructive and improved version of the proof that there exist a continuous map that solves the convexified problem is presented. A Lipschitz continuous map is analyzed such that a map vector minimizes the functional at each vector satisfying Cellina\\\'s condition of existence of minimum. This map is explicitly given by a direct constructive algorithm. %B Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717 %I SISSA %G en %U http://hdl.handle.net/1963/6439 %1 6379 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:52:31Z\\nNo. of bitstreams: 1\\nDM-Gon-Orn-96-sissa.pdf: 182850 bytes, checksum: e2288b2be15f6e2f0d0dfc3fc74af3cd (MD5) %R 10.1016/S0362-546X(98)00067-4 %0 Journal Article %J Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808 %D 1999 %T Renormalized solutions of elliptic equations with general measure data %A Gianni Dal Maso %A Francois Murat %A Luigi Orsina %A Alain Prignet %B Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808 %I Scuola Normale Superiore di Pisa %G en %U http://hdl.handle.net/1963/1236 %1 2707 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:08Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116 %D 1999 %T Some properties of the solutions of obstacle problems with measure data %A Paolo Dall'Aglio %A Gianni Dal Maso %B Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116 %G en %U http://hdl.handle.net/1963/6432 %1 6372 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:18:45Z\\nNo. of bitstreams: 1\\nDAgl-DM-98.pdf: 205798 bytes, checksum: 96a8209dd814b3087f68a24a5f79d5b5 (MD5) %0 Journal Article %J 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 Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %D 1998 %T Asymptotic behavior of nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %I SISSA Library %G en %U http://hdl.handle.net/1963/1064 %1 2738 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 %D 1998 %T Limits of variational problems for Dirichlet forms in varying domains %A Gianni Dal Maso %A Virginia De Cicco %A Lino Notarantonio %A Nicoletta A. Tchou %B Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116 %I SISSA %G en %U http://hdl.handle.net/1963/6440 %1 6377 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:44:35Z\\nNo. of bitstreams: 2\\nDM-DeC-96.pdf: 145467 bytes, checksum: 0cf974ac5cc090ff7f9faae3d433043f (MD5)\\nDM-DeC-96-cover.pdf: 35849 bytes, checksum: cde85af897042e1ee2c1b1a8c724b8eb (MD5) %R 10.1016/S0362-546X(98)00067-4 %0 Journal Article %J Potential Anal. 7 (1997), no. 4, 765-803 %D 1997 %T Capacity theory for monotone operators %A Gianni Dal Maso %A Igor V. Skrypnik %X If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$. %B Potential Anal. 7 (1997), no. 4, 765-803 %I Springer %G en %U http://hdl.handle.net/1963/911 %1 2880 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:40:26Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1023/A:1017987405983 %0 Journal Article %J Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277 %D 1997 %T Comportamento asintotico delle soluzioni di problemi di Dirichlet %A Gianni Dal Maso %B Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277 %G it %U http://hdl.handle.net/1963/6438 %1 6378 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:47:36Z\\nNo. of bitstreams: 1\\nDM-97-UMI.pdf: 232404 bytes, checksum: 9b45a539545e2635c8ffedf2ec7a0648 (MD5) %0 Journal Article %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396 %D 1997 %T Some properties of reachable solutions of nonlinear elliptic equations with measure data %A Gianni Dal Maso %A Annalisa Malusa %B Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396 %I SISSA %G en %U http://hdl.handle.net/1963/6434 %1 6375 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:33:05Z\\nNo. of bitstreams: 1\\nDM-Mal-97-sissa.pdf: 261079 bytes, checksum: bc786a00522c2b2dd3ee0acf0e9c3759 (MD5) %0 Journal Article %J Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 %D 1996 %T A capacity method for the study of Dirichlet problems for elliptic systems in varying domains %A Gianni Dal Maso %A Rodica Toader %B Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 %I SISSA Library %G en %U http://hdl.handle.net/1963/989 %1 2867 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:21Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %D 1995 %T Capacity and Dirichlet problems in varying domains %A Gianni Dal Maso %I SISSA Library %G en %U http://hdl.handle.net/1963/950 %1 3504 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:40:53Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %D 1995 %T Special functions of bounded deformation %A Giovanni Bellettini %A Alessandra Coscia %A Gianni Dal Maso %I SISSA Library %G en %U http://hdl.handle.net/1963/978 %1 3476 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 %D 1994 %T Limits of Dirichlet problems in perforated domains: a new formulation %A Gianni Dal Maso %A Rodica Toader %B Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360 %I Università degli Studi di Trieste, Dipartimento di Scienze Matematiche %G en_US %U http://hdl.handle.net/1963/3649 %1 656 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-16T11:02:31Z\\nNo. of bitstreams: 1\\ndalmaso18.pdf: 255148 bytes, checksum: e857ab6de9d63e187905170895a65ccf (MD5) %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 Appl.Math.Optim. 23 (1991), no.1, p. 17-49. %D 1991 %T Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions %A Giuseppe Buttazzo %A Gianni Dal Maso %B Appl.Math.Optim. 23 (1991), no.1, p. 17-49. %I SISSA Library %G en %U http://hdl.handle.net/1963/880 %1 2911 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:39:05Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Differential Integral Equations 4 (1991), no.4, p.739-765. %D 1991 %T On systems of ordinary differential equations with measures as controls %A Gianni Dal Maso %A Franco Rampazzo %B Differential Integral Equations 4 (1991), no.4, p.739-765. %I SISSA Library %G en %U http://hdl.handle.net/1963/840 %1 2951 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:35Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Differential Integral Equations 3 (1990), no.6, p.1151-1166. %D 1990 %T Correctors for the homogeneization of monotone operators %A Gianni Dal Maso %A Anneliese Defranceschi %B Differential Integral Equations 3 (1990), no.6, p.1151-1166. %I SISSA Library %G en %U http://hdl.handle.net/1963/812 %1 2979 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:16Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160 %D 1990 %T G-convergence of monotone operators %A Valeria Chiadò Piat %A Gianni Dal Maso %A Anneliese Defranceschi %B Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160 %I SISSA Library %G en %U http://hdl.handle.net/1963/680 %1 3246 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702 %D 1990 %T A general chain rule for distributional derivatives %A Luigi Ambrosio %A Gianni Dal Maso %B Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702 %I SISSA Library %G en %U http://hdl.handle.net/1963/650 %1 3276 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:52Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535. %D 1990 %T Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions %A Giuseppe Buttazzo %A Gianni Dal Maso %B Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535. %I SISSA Library %G en %U http://hdl.handle.net/1963/809 %1 2982 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:13Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. %D 1989 %T An approach to the thin obstacle problem for variational functionals depending on vector %A Gianni Dal Maso %A Roberta Musina %B Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. %I SISSA Library %G en %U http://hdl.handle.net/1963/802 %1 2989 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:08Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J J. Analyse Math. 53 (1989), 269--289 %D 1989 %T Convergence of unilateral problems for monotone operators %A Gianni Dal Maso %A Anneliese Defranceschi %B J. Analyse Math. 53 (1989), 269--289 %I SISSA Library %G en %U http://hdl.handle.net/1963/722 %1 3069 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:45Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 %D 1989 %T Limits of obstacle problems for the area functional. %A Gianni Dal Maso %A Michele Carriero %A Antonio Leaci %A Eduardo Pascali %B Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 %I SISSA Library %G en %U http://hdl.handle.net/1963/577 %1 3327 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:36Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1987 %0 Journal Article %J Acta Math. 163 (1989), no. 1-2, 57-107 %D 1989 %T A pointwise regularity theory for the two-obstacle problem %A Gianni Dal Maso %A Umberto Mosco %A Maria Agostina Vivaldi %B Acta Math. 163 (1989), no. 1-2, 57-107 %I SISSA Library %G en %U http://hdl.handle.net/1963/643 %1 3810 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:48Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135 %D 1988 %T A Kellogg property for µ-capacities %A Gianni Dal Maso %A Anneliese Defranceschi %B Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135 %I SISSA Library %G en %U http://hdl.handle.net/1963/492 %1 3412 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:34Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Manuscripta Math. 61 (1988), no. 3, 251-278. %D 1988 %T Limits of nonlinear Dirichlet problems in varying domains. %A Gianni Dal Maso %A Anneliese Defranceschi %X We study the general form of the limit, in the sense of gamma-convergence, of a sequence of nonlinear variational problems in varying domains with Dirichlet boudary conditions. The asymptotic problem is characterized in terms of the limit of suitable nonlinear capacities associated to the domains. %B Manuscripta Math. 61 (1988), no. 3, 251-278. %I SISSA Library %G en %U http://hdl.handle.net/1963/536 %1 3368 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:34:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J J.Funct.Anal. 79, 1988, no. 2, 476-492 %D 1988 %T Some properties of a class of nonlinear variational $m$-capacities %A Gianni Dal Maso %A Anneliese Defranceschi %B J.Funct.Anal. 79, 1988, no. 2, 476-492 %I SISSA Library %G en %U http://hdl.handle.net/1963/485 %1 3419 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:29Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %R 10.1016/0022-1236(88)90022-5 %0 Journal Article %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 Journal Article %J Ricerche Mat. 36 (1987), no. 2, 197-214 %D 1987 %T Integral representation of some convex local functionals. %A Gianni Dal Maso %A Gabriella Paderni %B Ricerche Mat. 36 (1987), no. 2, 197-214 %I SISSA Library %G en %U http://hdl.handle.net/1963/497 %1 3407 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:38Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118 %D 1987 %T Limits of nonlinear Dirichlet problems in varying domains. (Italian) %A Gianni Dal Maso %A Anneliese Defranceschi %B Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118 %I SISSA Library %G en %U http://hdl.handle.net/1963/486 %1 3418 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:30Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987 %0 Journal Article %J Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190 %D 1986 %T Convergence of unilateral convex sets. Optimization and related fields (Erice, 1984) %A Gianni Dal Maso %B Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190 %I SISSA Library %G en %U http://hdl.handle.net/1963/353 %1 3614 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:28:39Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1984 %0 Journal Article %J Nonlinear anal. 10(1986), no.6, 603-613 %D 1986 %T Dirichlet problems for demicoercive functionals %A Gabriele Anzellotti %A Giuseppe Buttazzo %A Gianni Dal Maso %B Nonlinear anal. 10(1986), no.6, 603-613 %I SISSA Library %G en %U http://hdl.handle.net/1963/390 %1 3577 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:31:55Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985 %R 10.1016/0362-546X(86)90145-8 %0 Journal Article %J J. Funct. Anal. 62 (1985), no. 2, 119--159 %D 1985 %T Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets %A Gianni Dal Maso %B J. Funct. Anal. 62 (1985), no. 2, 119--159 %I SISSA Library %G en %U http://hdl.handle.net/1963/318 %1 3649 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:28:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1984 %0 Journal Article %J Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985 %D 1985 %T Some singular perturbation problems in the calculus of variations. %A Gianni Dal Maso %B Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985 %I SISSA Library %G en %U http://hdl.handle.net/1963/297 %1 3670 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:27:46Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1983 %0 Journal Article %J Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106 %D 1985 %T Weak convergence of measures on spaces of semicontinuous functions. %A Gianni Dal Maso %A Ennio De Giorgi %A Luciano Modica %B Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106 %I SISSA Library %G en %U http://hdl.handle.net/1963/463 %1 3440 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:32:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985