The $\Gamma$-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension
Analysis of PDEs
2013-01-23 v1
Abstract
In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and -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.
Keywords
Cite
@article{arxiv.1301.5170,
title = {The $\Gamma$-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension},
author = {Giovanni Bellettini and Antonin Chambolle and Michael Goldman},
journal= {arXiv preprint arXiv:1301.5170},
year = {2013}
}