Finite-difference approximation of energies in fracture mechanics
Finite-differences discretizations of the Mumford-Shah functional
Finite-differences discretizations of the mumford-shah functional
About two years ago, Gobbino [21] gave a proof of a De Giorgi's conjecture on the approximation of the Mumford-Shah energy by means of finite-differences based non-local functionals. In this work, we introduce a discretized version of De Giorgi's approximation, that may be seen as a generalization of Blake and Zisserman's “weak membrane” energy (first introduced in the image segmentation framework). A simple adaptation of Gobbino's results allows us to compute the Γ-limit of this discrete functional...
Finite-tight sets
We introduce two notions of tightness for a set of measurable functions - the finite-tightness and the Jordan finite-tightness with the aim to extend certain compactness results (as biting lemma or Saadoune-Valadier’s theorem of stable compactness) to the unbounded case. These compactness conditions highlight their utility when we look for some alternatives to Rellich-Kondrachov theorem or relaxed lower semicontinuity of multiple integrals. Finite-tightness locates the great growths of a set of...
Flexible niveloids
Flow problems and duality.
Fréchet differentiability of Lipschitz functions via a variational principle
Free Discontinuity problems with unbounded Data: the two dimensional case.
Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design.
Functionals depending on curvatures with constraints
Functions of measures and a variational problem of the type of the nonparametric minimal surface
Funzioni -convesse
We study a class of functions which differ essentially from those which are the sum of a convex function and a regular one and which have interesting properties related to -convergence and to problems with non-convex constraints. In particular some results are given for the associated evolution equations.
Funzioni semiconcave, singolarità e pile di sabbia
La semiconcavità è una nozione che generalizza quella di concavità conservandone la maggior parte delle proprietà ma permettendo di ampliarne le applicazioni. Questa è una rassegna dei punti più salienti della teoria delle funzioni semiconcave, con particolare riguardo allo studio dei loro insiemi singolari. Come applicazione, si discuterà una formula di rappresentazione per la soluzione di un modello dinamico per la materia granulare.
Further remarks on the lower semicontinuity of polyconvex integrals
Further results related to a minimax problem of Ricceri.
Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional
We establish some new results about the Γ-limit, with respect to the L1-topology, of two different (but related) phase-field approximations ℰ ε ε , x10ff65; ℰ ε ε of the so-called Euler’s Elastica Bending Energy for curves in the plane. In particular we characterize theΓ-limit as ε → 0 of ℰε, and show that in general the Γ-limits of ℰεand x10ff65; ℰ ε do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of theΓ-limit of x10ff65;...
Gap phenomenon for some autonomous functionals.
General method of regularization. I: Functionals defined on BD space
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. In part II, we will show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we will prove the existence theorem for the limit analysis problem.
General method of regularization. II: Relaxation proposed by suquet
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. We show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we prove an existence theorem for the limit analysis problem.
General method of regularization. III: The unilateral contact problem
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material with the Signorini constraints on the boundary) is the weak* lower semicontinuous regularization of the plastic energy. We consider an elastic-plastic solid endowed with the von Mises (or Tresca) yield condition. Moreover, we show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. We deduce that...