vix.ing · top · new · best · stats · spec

The Γ-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension

2013/01/22 by Bellettini, Giovanni, Chambolle, Antonin, Goldman, Michael · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1301.5170

Abstract

In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and Γ-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the space of special functions of bounded variation with vanishing diffuse gradient part. This provides a direction of investigation to derive approximation for functionals with discontinuities penalized with a "cohesive" energy, that is, whose cost depends on the actual opening of the discontinuity.

Cited by

Related