An extension theorem in SBV and an application to the homogenization of the Mumford-Shah functional in perforated domains

The aim of this paper is to prove the existence of extension operators for SBV functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a non coercive homogenization problem

A stability result for nonlinear Neumann problems under boundary variations

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.Comment: 26 page

Finite element approximation of non-isotropic free-discontinuity problems

We study a discretization procedure, using finite elements, for a class of non-isotropic free-discontinuity problems based on the non-local approximation we proposed in a previous paper

A new approximation result for BV-functions

This Note is devoted to obtaining an approximation result for \BV-functions by means of a quasi-polyhedral sequence of \BV-functions. This approximation could have interesting applications in some problems of the Calculus of Variation

A density result in SBV with respect to non-isotropic energies

In this paper weshow that any bounded function in SBV can be approximated by functions which have polyhedral jump set and are smooth, in such a way that the difference of the corresponding values of a large class of lower semicontinuous functionals tends to zero along the approximating sequence

An approximation result for free discontinuity functionals by means of non-local energies

We approximate, in the sense of Gamma-convergence, free discontinuity functionals with linear growth by a sequence of non-local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186(4): 722\u2013744), where there is the proof of the general one-dimensional case, and in (ESAIM Control Optim. Calc. Var. 2007; 13(1):135\u2013162), where a particular n-dimensional case is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non-local energies

Sequences of non-local functionals which approximate free-discontinuity problems

Biblioteca Centrale CNR / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

A numerical approach to image segmentation problems

Consiglio Nazionale delle Ricerche - Biblioteca Centrale -. P.le Aldo Moro, 7, Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Strong approximation of GSBV functions by piecewise smooth functions

Consiglio Nazionale delle Ricerche - Biblioteca Centrale -. P.le Aldo Moro, 7, Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal