We 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.

}, doi = {10.1016/j.matpur.2017.05.018}, url = {http://hdl.handle.net/20.500.11767/15979}, author = {Stefano Almi and Gianni Dal Maso and Rodica Toader} } @article {2016, title = {Existence and uniqueness of dynamic evolutions for a peeling test in dimension one}, number = {Preprint;05/2016/MATE}, year = {2016}, institution = {SISSA}, abstract = {In 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.

}, url = {http://urania.sissa.it/xmlui/handle/1963/35168}, author = {Gianni Dal Maso and Giuliano Lazzaroni and Lorenzo Nardini} } @article {2016, title = {A model for the quasistatic growth of cracks with fractional dimension}, number = {SISSA;10/2016/MATE}, year = {2016}, abstract = {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.}, url = {http://urania.sissa.it/xmlui/handle/1963/35175}, author = {Gianni Dal Maso and Marco Morandotti} } @article {2015, title = {Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition}, year = {2015}, abstract = {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.}, url = {http://urania.sissa.it/xmlui/handle/1963/35045}, author = {Gianni Dal Maso and Cristopher J. Larsen and Rodica Toader} } @article {2015, title = {Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation}, number = {SISSA;43/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We study the lower semicontinuity of some free discontinuity functionals, whose volume term depends on the Euclidean norm of the symmetrized gradient.}, url = {http://urania.sissa.it/xmlui/handle/1963/34533}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @article {2015, title = {The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data}, number = {SISSA;47/2015/MATE}, year = {2015}, abstract = {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.}, url = {http://urania.sissa.it/xmlui/handle/1963/34629}, author = {Gianni Dal Maso and Ilaria Lucardesi} } @article {2014, title = {Editorial}, number = {Rendiconti del circolo matematico di Palermo;volume 63; issue 3; pages 317-318;}, year = {2014}, publisher = {Springer}, doi = {10.1007/s12215-014-0172-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34712}, author = {Ciro Ciliberto and Gianni Dal Maso and Pasquale Vetro} } @article {2014, title = {Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length}, number = {Nonlinear Differential Equations and Applications}, year = {2014}, publisher = {SISSA}, abstract = {We 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.}, keywords = {cracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions}, doi = {10.1007/s00030-014-0291-0}, url = {http://hdl.handle.net/1963/7271}, author = {Gianni Dal Maso and Gianluca Orlando and Rodica Toader} } @article {2012, title = {New results on Gamma-limits of integral functionals}, number = {Annales de l{\textquoteright}Institut Henri Poincare. Analyse Non Lineaire}, year = {2014}, publisher = {Elsevier}, keywords = {Gamma-convergence}, doi = {10.1016/j.anihpc.2013.02.005}, url = {http://hdl.handle.net/1963/5880}, author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri} } @article {2014, title = {Quasi-static crack growth in hydraulic fracture}, journal = {Nonlinear Analysis}, volume = {109}, number = {Nonlinear Analysis, Theory, Methods and Applications;109}, year = {2014}, pages = {301-318}, publisher = {Elsevier}, type = {Journal article}, chapter = {301}, abstract = {We 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.

}, doi = {10.1016/j.na.2014.07.009}, url = {http://hdl.handle.net/20.500.11767/17350}, author = {Stefano Almi and Gianni Dal Maso and Rodica Toader} } @article {2013, title = {Quasistatic evolution in perfect plasticity as limit of dynamic processes}, number = {Journal of Dynamics and Differential Equations}, year = {2014}, publisher = {SISSA}, abstract = {We introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and we 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.}, keywords = {visco-elasto-plasticity}, doi = {10.1007/s10884-014-9409-7}, url = {http://hdl.handle.net/1963/6982}, author = {Gianni Dal Maso and Riccardo Scala} } @article {2014, title = {Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional}, year = {2014}, note = {This article is composed if 33 pages and recorded in PDF format}, publisher = {SISSA}, abstract = {The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.}, keywords = {Gamma-convergence, Cahn-Hilliard functional, phase transitions}, url = {http://hdl.handle.net/1963/7390}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2013, title = {Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces}, number = {Archive for Rational Mechanics and Analysis}, year = {2013}, publisher = {Springer}, abstract = {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].}, keywords = {singular nonlinear parabolic equations, Hilbert transform, thin films}, doi = {10.1007/s00205-014-0730-4}, url = {http://hdl.handle.net/1963/7245}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2013, title = {Attainment results for nematic elastomers}, year = {2013}, institution = {SISSA}, abstract = {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.}, url = {http://hdl.handle.net/1963/7174}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2013, title = {Fracture models as Gamma-limits of damage models}, journal = {Communications on Pure and Applied Analysis 12 (2013) 1657-1686}, number = {SISSA;25/2011/M}, year = {2013}, publisher = {American Institute of Mathematical Sciences}, abstract = {We 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.}, doi = {10.3934/cpaa.2013.12.1657}, url = {http://hdl.handle.net/1963/4225}, author = {Gianni Dal Maso and Flaviana Iurlano} } @article {2013, title = {One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls}, number = {arXiv:1302.0901;}, year = {2013}, publisher = {SISSA}, abstract = {In 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.}, url = {http://hdl.handle.net/1963/6467}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @article {2012, title = {Gamma-convergence and H-convergence of linear elliptic operators}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es, Available online 12 September 2012}, number = {SISSA;04/2012/M}, year = {2012}, publisher = {Elsevier}, keywords = {Linear elliptic operators}, doi = {10.1016/j.matpur.2012.09.004}, url = {http://hdl.handle.net/1963/5878}, author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri} } @article {2012, title = {Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 29 (2012) 715-735}, number = {SISSA;30/2011/M}, year = {2012}, publisher = {Gauthier-Villars;Elsevier}, abstract = {The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.anihpc.2012.04.001}, url = {http://hdl.handle.net/1963/4267}, author = {Virginia Agostiniani and Gianni Dal Maso and Antonio DeSimone} } @article {2012, title = {Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution}, journal = {Calculus of variations and partial differential equations 44 (2012) 495-541}, number = {SISSA;46/2010/M}, year = {2012}, publisher = {Springer}, abstract = {Cam-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.}, doi = {10.1007/s00526-011-0443-6}, url = {http://hdl.handle.net/1963/3900}, author = {Gianni Dal Maso and Antonio DeSimone and Francesco Solombrino} } @article {2011, title = {Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem}, journal = {Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231}, number = {SISSA;70/2009/M}, year = {2011}, publisher = {American Institute of Mathematical Sciences}, abstract = {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.}, doi = {10.3934/dcds.2011.31.1219}, url = {http://hdl.handle.net/1963/3801}, author = {Gianni Dal Maso and Giuliano Lazzaroni} } @article {2011, title = {Ennio De Giorgi and Γ-convergence}, journal = {Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021}, year = {2011}, publisher = {American Institute of Mathematical Sciences}, abstract = {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.}, doi = {10.3934/dcds.2011.31.1017}, url = {http://hdl.handle.net/1963/5308}, author = {Gianni Dal Maso} } @article {2011, title = {An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers}, journal = {SIAM J. Math. Anal. 43 (2011) 1345-1368}, number = {SISSA;44/2010/M}, year = {2011}, publisher = {Society for Industrial and Applied Mathematics}, abstract = {We 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.}, doi = {10.1137/10080083X}, url = {http://hdl.handle.net/1963/3894}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @article {2011, title = {Existence for wave equations on domains with arbitrary growing cracks}, journal = {Rend. Lincei Mat. Appl. 22 (2011) 387-408}, number = {SISSA;32/2011/M}, year = {2011}, publisher = {European Mathematical Society}, abstract = {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.}, keywords = {Wave equation}, doi = {10.4171/RLM/606}, url = {http://hdl.handle.net/1963/4284}, author = {Gianni Dal Maso and Cristopher J. Larsen} } @article {9991, title = {Generalised functions of bounded deformation}, journal = {J. Eur. Math. Soc. (JEMS), to appear}, year = {2011}, publisher = {SISSA}, abstract = {We 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.

}, keywords = {free discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability}, url = {http://hdl.handle.net/1963/6374}, author = {Gianni Dal Maso} } @article {2011, title = {Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling}, journal = {Calculus of Variations and Partial Differential Equations 40 (2011) 125-181}, number = {SISSA;36/2009/M}, year = {2011}, publisher = {Springer}, abstract = {Cam-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.}, keywords = {Cam-Clay plasticity}, doi = {10.1007/s00526-010-0336-0}, url = {http://hdl.handle.net/1963/3670}, author = {Gianni Dal Maso and Antonio DeSimone and Francesco Solombrino} } @article {2011, title = {Singular perturbation models in phase transitions for second order materials}, journal = {Indiana Univ. Math. J. 60 (2011) 367-409}, number = {SISSA;20/2010/M}, year = {2011}, publisher = {Indiana University}, abstract = {A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.}, doi = {10.1512/iumj.2011.60.4346}, url = {http://hdl.handle.net/1963/3858}, author = {Milena Chermisi and Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2010, title = {Homogenization of fiber reinforced brittle material: the intermediate case}, journal = {Adv. Calc. Var. 3 (2010) 345-370}, number = {SISSA;14/2009/M}, year = {2010}, publisher = {Walter de Gruyter}, abstract = {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.}, doi = {10.1515/ACV.2010.011}, url = {http://hdl.handle.net/1963/3607}, author = {Gianni Dal Maso and Caterina Ida Zeppieri} } @article {2010, title = {Nonlocal character of the reduced theory of thin films with higher order perturbations}, journal = {Adv. Calc. Var. 3 (2010) 287-319}, number = {SISSA;57/2009/M}, year = {2010}, doi = {10.1515/ACV.2010.012, /July/2010}, url = {http://hdl.handle.net/1963/3754}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {2010, title = {Quasistatic crack growth in elasto-plastic materials: the two-dimensional case}, journal = {Arch. Ration. Mech. Anal. 196 (2010) 867-906}, number = {SISSA;62/2008/M}, year = {2010}, abstract = {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.}, doi = {10.1007/s00205-009-0258-1}, url = {http://hdl.handle.net/1963/2964}, author = {Gianni Dal Maso and Rodica Toader} } @article {2010, title = {Quasistatic crack growth in finite elasticity with non-interpenetration}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290}, number = {SISSA;80/2008/M}, year = {2010}, abstract = {We 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.

}, doi = {10.1016/j.anihpc.2009.09.006}, url = {http://hdl.handle.net/1963/3397}, author = {Gianni Dal Maso and Giuliano Lazzaroni} } @article {2010, title = {Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case}, journal = {Netw. Heterog. Media 5 (2010) 97-132}, number = {SISSA;39/2009/M}, year = {2010}, abstract = {We 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.}, keywords = {Cam-Clay plasticity}, doi = {10.3934/nhm.2010.5.97}, url = {http://hdl.handle.net/1963/3671}, author = {Gianni Dal Maso and Francesco Solombrino} } @article {2009, title = {A higher order model for image restoration: the one dimensional case}, journal = {SIAM J. Math. Anal. 40 (2009) 2351-2391}, number = {SISSA;66/2008/M}, year = {2009}, abstract = {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.}, doi = {10.1137/070697823}, url = {http://hdl.handle.net/1963/3174}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini} } @article {2009, title = {Homogenization of fiber reinforced brittle materials: the extremal cases}, journal = {SIAM J. Math. Anal. 41 (2009) 1874-1889}, number = {SISSA;49/2008/M}, year = {2009}, publisher = {SIAM}, abstract = {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.}, url = {http://hdl.handle.net/1963/2705}, author = {Marco Barchiesi and Gianni Dal Maso} } @article {2009, title = {Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions}, journal = {Math. Models Methods Appl. Sci. 19 (2009) 1643-1711}, number = {SISSA;78/2008/M}, year = {2009}, abstract = {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.}, doi = {10.1142/S0218202509003942}, url = {http://hdl.handle.net/1963/3395}, author = {Gianni Dal Maso and Antonio DeSimone} } @article {2009, title = {A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions}, journal = {Boll. Unione Mat. Ital. (9) 2 (2009) 371-390}, number = {SISSA;41/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2675}, author = {Gianni Dal Maso and Alessandro Giacomini and Marcello Ponsiglione} } @article {2008, title = {Decomposition results for functions with bounded variation}, journal = {Boll. Unione Mat. Ital. (9) 1 (2008) 497-505}, year = {2008}, publisher = {Unione Matematica Italiana}, url = {http://hdl.handle.net/1963/3535}, author = {Gianni Dal Maso and Rodica Toader} } @article {2008, title = {Globally stable quasistatic evolution in plasticity with softening}, journal = {Netw. Heterog. Media 3 (2008) 567-614}, number = {SISSA;23/2007/M}, year = {2008}, abstract = {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.}, url = {http://hdl.handle.net/1963/1965}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2008, title = {Gradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics}, journal = {Calc. Var. Partial Differential Equations 31 (2008) 137-145}, number = {SISSA;50/2005/M}, year = {2008}, abstract = {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.}, doi = {10.1007/s00526-006-0084-3}, url = {http://hdl.handle.net/1963/1723}, author = {Gianni Dal Maso and Adriana Garroni} } @article {2008, title = {A vanishing viscosity approach to quasistatic evolution in plasticity with softening}, journal = {Arch. Ration. Mech. Anal. 189 (2008) 469-544}, number = {SISSA;38/2006/M}, year = {2008}, abstract = {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.}, doi = {10.1007/s00205-008-0117-5}, url = {http://hdl.handle.net/1963/1844}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2007, title = {On a notion of unilateral slope for the Mumford-Shah functional}, journal = {NoDEA 13 (2007) 713-734}, number = {SISSA;78/2004/M}, year = {2007}, abstract = {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.}, doi = {10.1007/s00030-006-4054-4}, url = {http://hdl.handle.net/1963/2059}, author = {Gianni Dal Maso and Rodica Toader} } @article {2007, title = {Quasistatic crack growth for a cohesive zone model with prescribed crack path}, number = {SISSA;44/2005/M}, year = {2007}, abstract = {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.}, doi = {10.1017/S030821050500079X}, url = {http://hdl.handle.net/1963/1686}, author = {Gianni Dal Maso and Chiara Zanini} } @article {2007, title = {Quasistatic evolution problems for pressure-sensitive plastic materials}, journal = {Milan J. Math. 75 (2007) 117-134}, number = {SISSA;27/2007/M}, year = {2007}, abstract = {We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity.}, doi = {10.1007/s00032-007-0071-y}, url = {http://hdl.handle.net/1963/1962}, author = {Gianni Dal Maso and Alexey Demyanov and Antonio DeSimone} } @article {2007, title = {Time-dependent systems of generalized Young measures}, number = {SISSA;98/2005/M}, year = {2007}, abstract = {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.}, url = {http://hdl.handle.net/1963/1795}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2006, title = {Quasistatic evolution problems for linearly elastic-perfectly plastic materials}, journal = {Arch. Ration. Mech. Anal. 180 (2006) 237-291}, number = {arXiv.org;math/0412212v1}, year = {2006}, abstract = {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.}, doi = {10.1007/s00205-005-0407-0}, url = {http://hdl.handle.net/1963/2129}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora} } @article {2006, title = {Variational problems in fracture mechanics}, number = {SISSA;10/2006/M}, year = {2006}, abstract = {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.}, url = {http://hdl.handle.net/1963/1816}, author = {Gianni Dal Maso} } @article {2005, title = {Quasistatic Crack Growth in Nonlinear Elasticity}, journal = {Arch. Ration. Mech. Anal. 176 (2005) 165-225}, number = {SISSA;2/2004/M}, year = {2005}, abstract = {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.}, doi = {10.1007/s00205-004-0351-4}, url = {http://hdl.handle.net/1963/2293}, author = {Gianni Dal Maso and Gilles A. Francfort and Rodica Toader} } @booklet {2005, title = {Solutions of Neumann problems in domains with cracks and applications to fracture mechanics}, number = {arXiv.org;math.AP/0105132}, year = {2005}, url = {http://hdl.handle.net/1963/1684}, author = {Gianni Dal Maso} } @article {2004, title = {Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains}, journal = {Ann. Inst. H. Poincar{\'e}. Anal. Non Lin{\'e}aire 21 (2004), (4), p. 445-486.}, number = {SISSA;40/2002/M}, year = {2004}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/1611}, author = {Gianni Dal Maso and Francois Murat} } @article {2004, title = {Higher order quasiconvexity reduces to quasiconvexity}, journal = {Arch. Ration. Mech. Anal. 171 (2004) 55-81}, number = {SISSA;41/2003/M}, year = {2004}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/s00205-003-0278-1}, url = {http://hdl.handle.net/1963/2911}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini} } @article {2004, title = {Quasi-static evolution in brittle fracture: the case of bounded solutions}, journal = {Quad. Mat. Dip. Mat. Seconda Univ. Napoli 14 (2004) 245-266}, number = {SISSA;3/2004/M}, year = {2004}, abstract = {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 $L^\\\\infty$.}, url = {http://hdl.handle.net/1963/2229}, author = {Gianni Dal Maso and Gilles A. Francfort and Rodica Toader} } @article {2003, title = {Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations}, journal = {Applied Math.Optim. 48 (2003), no.1, p.39-66}, number = {SISSA;55/2002/M}, year = {2003}, publisher = {SISSA Library}, doi = {10.1007/s00245-003-0768-4}, url = {http://hdl.handle.net/1963/1625}, author = {Gianni Dal Maso and Helene Frankowska} } @article {2003, title = {The calibration method for the Mumford-Shah functional and free-discontinuity problems}, journal = {Calc. Var. Partial Differential Equations 16 (2003) 299-333}, number = {SISSA;35/2001/M}, year = {2003}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/s005260100152}, url = {http://hdl.handle.net/1963/3051}, author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso} } @article {2003, title = {A stability result for nonlinear Neumann problems under boundary variations}, journal = {J.Math. Pures Appl. (9) 82 (2003) no.5 , 503}, number = {SISSA;48/2002/M}, year = {2003}, publisher = {SISSA Library}, abstract = {In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.}, doi = {10.1016/S0021-7824(03)00014-X}, url = {http://hdl.handle.net/1963/1618}, author = {Gianni Dal Maso and Francois Ebobisse and Marcello Ponsiglione} } @article {2002, title = {Linearized elasticity as gamma-limit of finite elasticity}, journal = {Set-Valued Anal. 10 (2002), p.165-183}, number = {SISSA;69/2001/M}, year = {2002}, publisher = {Springer}, doi = {10.1023/A:1016577431636}, url = {http://hdl.handle.net/1963/3052}, author = {Gianni Dal Maso and Matteo Negri and Danilo Percivale} } @article {2002, title = {A model for the quasi-static growth of a brittle fracture: existence and approximation results}, journal = {Math. Models Methods Appl. Sci., 12 (2002), no. 12, 1773}, number = {SISSA;115/00/M}, year = {2002}, publisher = {SISSA Library}, abstract = {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.}, doi = {10.1142/S0218202502002331}, url = {http://hdl.handle.net/1963/1571}, author = {Gianni Dal Maso and Rodica Toader} } @article {2002, title = {A model for the quasi-static growth of brittle fractures based on local minimization}, journal = {Math.Models Methods Appl. Sci., 12 (2002) , p.1773-1800.}, number = {SISSA;51/2002/M}, year = {2002}, publisher = {SISSA Library}, abstract = {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.}, doi = {10.1142/S0218202502002331}, url = {http://hdl.handle.net/1963/1621}, author = {Gianni Dal Maso and Rodica Toader} } @article {2002, title = {A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results}, journal = {Arch. Ration. Mech. Anal. 162 (2002) 101-135}, number = {SISSA;30/2001/M}, year = {2002}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/s002050100187}, url = {http://hdl.handle.net/1963/3056}, author = {Gianni Dal Maso and Rodica Toader} } @article {2001, title = {Gamma-limit of periodic obstacles}, journal = {Acta Appl. Math., 2001, 65, 207-215}, number = {SISSA;37/00/M}, year = {2001}, publisher = {SISSA Library}, abstract = {We compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles.}, doi = {10.1023/A:1010668530972}, url = {http://hdl.handle.net/1963/1495}, author = {Gianni Dal Maso and Paola Trebeschi} } @article {2001, title = {A monotonicity approach to nonlinear Dirichlet problems in perforated domains}, journal = {Adv. Math. Sci. Appl. 11 (2001) 721-751}, number = {SISSA;99/00/M}, year = {2001}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/1555}, author = {Gianni Dal Maso and Igor V. Skrypnik} } @article {2001, title = {Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations}, journal = {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}, number = {SISSA;57/00/M}, year = {2001}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/1515}, author = {Gianni Dal Maso and Helene Frankowska} } @article {2000, title = {The Calibration Method for Free Discontinuity Problems}, journal = {European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326.}, number = {SISSA;38/00/M}, year = {2000}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/1496}, author = {Gianni Dal Maso} } @article {2000, title = {Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets}, journal = {J. Math. Pures Appl. 79, 2 (2000) 141-162}, number = {SISSA;47/99/M}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0021-7824(99)00140-3}, url = {http://hdl.handle.net/1963/1261}, author = {Gianni Dal Maso and Maria Giovanna Mora and Massimiliano Morini} } @article {2000, title = {Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities}, journal = {ESAIM Control Optim. Calc. Var., 5 (2000), n. 5, p. 369-393.}, number = {SISSA;56/00/M}, year = {2000}, publisher = {SISSA Library}, doi = {10.1051/cocv:2000114}, url = {http://hdl.handle.net/1963/1514}, author = {Gianni Dal Maso and Helene Frankowska} } @article {1999, title = {Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains}, journal = {Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112}, year = {1999}, isbn = {1618-1891}, doi = {10.1007/BF01759365}, url = {http://hdl.handle.net/1963/6433}, author = {Gianni Dal Maso and Igor V. Skrypnik} } @article {1999, title = {The calibration method for the Mumford-Shah functional}, journal = {C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254}, number = {SISSA;21/99/M}, year = {1999}, publisher = {Elsevier}, abstract = {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).}, doi = {10.1016/S0764-4442(00)88602-4}, url = {http://hdl.handle.net/1963/1235}, author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso} } @article {1999, title = {Discrete approximation of the Mumford-Shah functional in dimension two}, journal = {M2AN 33 (1999) 651-672}, year = {1999}, publisher = {EDP Sciences}, doi = {10.1051/m2an:1999156}, url = {http://hdl.handle.net/1963/3588}, author = {Antonin Chambolle and Gianni Dal Maso} } @article {1999, title = {Evans-Vasilesco theorem in Dirichlet spaces}, journal = {Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15}, year = {1999}, publisher = {SISSA}, url = {http://hdl.handle.net/1963/6436}, author = {Gianni Dal Maso and Virginia De Cicco} } @article {1999, title = {A Lipschitz selection from the set of minimizers of a nonconvex functional of the gradient}, journal = {Nonlinear Analysis, Theory, Methods and Applications. Volume 37, Issue 6, September 1999, Pages 707-717}, year = {1999}, publisher = {SISSA}, abstract = {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.}, doi = {10.1016/S0362-546X(98)00067-4}, url = {http://hdl.handle.net/1963/6439}, author = {Gianni Dal Maso and Vladimir V. Goncharov and Antonio Ornelas} } @article {1999, title = {Renormalized solutions of elliptic equations with general measure data}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808}, number = {SISSA;22/99/M}, year = {1999}, publisher = {Scuola Normale Superiore di Pisa}, url = {http://hdl.handle.net/1963/1236}, author = {Gianni Dal Maso and Francois Murat and Luigi Orsina and Alain Prignet} } @article {1999, title = {Some properties of the solutions of obstacle problems with measure data}, journal = {Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116}, year = {1999}, url = {http://hdl.handle.net/1963/6432}, author = {Paolo Dall{\textquoteright}Aglio and Gianni Dal Maso} } @article {1999, title = {Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case}, journal = {Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58}, number = {SISSA;160/97/M}, year = {1999}, publisher = {Springer}, abstract = {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.}, doi = {10.1007/s002050050135}, url = {http://hdl.handle.net/1963/3371}, author = {Andrea Braides and Gianni Dal Maso and Adriana Garroni} } @article {1998, title = {Asymptotic behavior of nonlinear Dirichlet problems in perforated domains}, journal = {Ann. Mat. Pura Appl. (4) 174 (1998), 13--72}, number = {SISSA;162/95/M}, year = {1998}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1064}, author = {Gianni Dal Maso and Igor V. Skrypnik} } @article {1998, title = {Limits of variational problems for Dirichlet forms in varying domains}, journal = {Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116}, year = {1998}, publisher = {SISSA}, doi = {10.1016/S0362-546X(98)00067-4}, url = {http://hdl.handle.net/1963/6440}, author = {Gianni Dal Maso and Virginia De Cicco and Lino Notarantonio and Nicoletta A. Tchou} } @article {1997, title = {Capacity theory for monotone operators}, journal = {Potential Anal. 7 (1997), no. 4, 765-803}, number = {SISSA;6/95/M}, year = {1997}, publisher = {Springer}, abstract = {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 $F$.}, doi = {10.1023/A:1017987405983}, url = {http://hdl.handle.net/1963/911}, author = {Gianni Dal Maso and Igor V. Skrypnik} } @article {1997, title = {Comportamento asintotico delle soluzioni di problemi di Dirichlet}, journal = {Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277}, year = {1997}, note = {This is the title of the conference which was delivered by prof. Dal Maso in Padova during the XV Congress of the \\\"Unione Mathematica Italiana\\\" (Padova, 11-16 settembre 1995)}, url = {http://hdl.handle.net/1963/6438}, author = {Gianni Dal Maso} } @article {1997, title = {Some properties of reachable solutions of nonlinear elliptic equations with measure data}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. S{\'e}r. 4, 25 no. 1-2 (1997), p. 375-396}, year = {1997}, publisher = {SISSA}, url = {http://hdl.handle.net/1963/6434}, author = {Gianni Dal Maso and Annalisa Malusa} } @article {1996, title = {A capacity method for the study of Dirichlet problems for elliptic systems in varying domains}, journal = {Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277}, number = {SISSA;87/95/M}, year = {1996}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/989}, author = {Gianni Dal Maso and Rodica Toader} } @article {1995, title = {Capacity and Dirichlet problems in varying domains}, number = {SISSA;47/95/M}, year = {1995}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/950}, author = {Gianni Dal Maso} } @article {1995, title = {Special functions of bounded deformation}, number = {SISSA;76/95/M}, year = {1995}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/978}, author = {Giovanni Bellettini and Alessandra Coscia and Gianni Dal Maso} } @article {1994, title = {Limits of Dirichlet problems in perforated domains: a new formulation}, journal = {Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360}, number = {SISSA;167/1994/M}, year = {1994}, publisher = {Universit{\`a} degli Studi di Trieste, Dipartimento di Scienze Matematiche}, url = {http://hdl.handle.net/1963/3649}, author = {Gianni Dal Maso and Rodica Toader} } @article {1992, title = {A variational method in image segmentation: existence and approximation result}, journal = {Acta Math. 168 (1992), no.1-2, p. 89-151}, number = {SISSA;48/89/M}, year = {1992}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/808}, author = {Gianni Dal Maso and Jean-Michel Morel and Sergio Solimini} } @article {1991, title = {Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions}, journal = {Appl.Math.Optim. 23 (1991), no.1, p. 17-49.}, number = {SISSA;124/89/M}, year = {1991}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/880}, author = {Giuseppe Buttazzo and Gianni Dal Maso} } @article {1991, title = {On systems of ordinary differential equations with measures as controls}, journal = {Differential Integral Equations 4 (1991), no.4, p.739-765.}, number = {SISSA;82/89/M}, year = {1991}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/840}, author = {Gianni Dal Maso and Franco Rampazzo} } @article {1990, title = {Correctors for the homogeneization of monotone operators}, journal = {Differential Integral Equations 3 (1990), no.6, p.1151-1166.}, number = {SISSA;52/89/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/812}, author = {Gianni Dal Maso and Anneliese Defranceschi} } @article {1990, title = {G-convergence of monotone operators}, journal = {Ann. Inst. H. Poincare\\\' Anal. Non Lin{\'e}re 7 (1990), no. 3, 123-160}, number = {SISSA;84/88/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/680}, author = {Valeria Chiad{\`o} Piat and Gianni Dal Maso and Anneliese Defranceschi} } @article {1990, title = {A general chain rule for distributional derivatives}, journal = {Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702}, number = {SISSA;54/88/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/650}, author = {Luigi Ambrosio and Gianni Dal Maso} } @article {1990, title = {Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions}, journal = {Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535.}, number = {SISSA;49/89/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/809}, author = {Giuseppe Buttazzo and Gianni Dal Maso} } @article {1989, title = {An approach to the thin obstacle problem for variational functionals depending on vector}, journal = {Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743.}, number = {SISSA;41/89/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/802}, author = {Gianni Dal Maso and Roberta Musina} } @article {1989, title = {Convergence of unilateral problems for monotone operators}, journal = {J. Analyse Math. 53 (1989), 269--289}, number = {SISSA;126/88/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/722}, author = {Gianni Dal Maso and Anneliese Defranceschi} } @article {1989, title = {Limits of obstacle problems for the area functional.}, journal = {Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309}, number = {SISSA;96/87/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/577}, author = {Gianni Dal Maso and Michele Carriero and Antonio Leaci and Eduardo Pascali} } @article {1989, title = {A pointwise regularity theory for the two-obstacle problem}, journal = {Acta Math. 163 (1989), no. 1-2, 57-107}, number = {SISSA;47/88/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/643}, author = {Gianni Dal Maso and Umberto Mosco and Maria Agostina Vivaldi} } @article {1988, title = {A Kellogg property for {\textmu}-capacities}, journal = {Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135}, number = {SISSA;10/87/M}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/492}, author = {Gianni Dal Maso and Anneliese Defranceschi} } @article {1988, title = {Limits of nonlinear Dirichlet problems in varying domains.}, journal = {Manuscripta Math. 61 (1988), no. 3, 251-278.}, number = {SISSA;54/87/A}, year = {1988}, publisher = {SISSA Library}, abstract = {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.}, url = {http://hdl.handle.net/1963/536}, author = {Gianni Dal Maso and Anneliese Defranceschi} } @article {1988, title = {Some properties of a class of nonlinear variational $m$-capacities}, journal = {J.Funct.Anal. 79, 1988, no. 2, 476-492}, number = {SISSA;3/87/M}, year = {1988}, publisher = {SISSA Library}, doi = {10.1016/0022-1236(88)90022-5}, url = {http://hdl.handle.net/1963/485}, author = {Gianni Dal Maso and Anneliese Defranceschi} } @article {1988, title = {Variational inequalities for the biharmonic operator with variable obstacles.}, journal = {Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989)}, number = {SISSA;50/87/M}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/531}, author = {Gianni Dal Maso and Gabriella Paderni} } @article {1987, title = {Integral representation of some convex local functionals.}, journal = {Ricerche Mat. 36 (1987), no. 2, 197-214}, number = {SISSA;15/87/M}, year = {1987}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/497}, author = {Gianni Dal Maso and Gabriella Paderni} } @article {1987, title = {Limits of nonlinear Dirichlet problems in varying domains. (Italian)}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118}, number = {SISSA;4/87/M}, year = {1987}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/486}, author = {Gianni Dal Maso and Anneliese Defranceschi} } @article {1986, title = {Convergence of unilateral convex sets. Optimization and related fields (Erice, 1984)}, journal = {Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190}, number = {SISSA;50/84/M}, year = {1986}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/353}, author = {Gianni Dal Maso} } @article {1986, title = {Dirichlet problems for demicoercive functionals}, journal = {Nonlinear anal. 10(1986), no.6, 603-613}, number = {SISSA;03/85/M}, year = {1986}, publisher = {SISSA Library}, doi = {10.1016/0362-546X(86)90145-8}, url = {http://hdl.handle.net/1963/390}, author = {Gabriele Anzellotti and Giuseppe Buttazzo and Gianni Dal Maso} } @article {1985, title = {Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets}, journal = {J. Funct. Anal. 62 (1985), no. 2, 119--159}, number = {SISSA;15/84/M}, year = {1985}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/318}, author = {Gianni Dal Maso} } @article {1985, title = {Some singular perturbation problems in the calculus of variations.}, journal = {Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985}, number = {SISSA;62/83/M}, year = {1985}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/297}, author = {Gianni Dal Maso} } @article {1985, title = {Weak convergence of measures on spaces of semicontinuous functions.}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106}, number = {SISSA;76/85/MP}, year = {1985}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/463}, author = {Gianni Dal Maso and Ennio De Giorgi and Luciano Modica} }