Calculus of Variations and Geometric Measure Theory

G. Bellettini - A. Chambolle - M. Goldman

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

created by goldman on 22 Jan 2013
modified on 17 Jun 2013


Accepted Paper

Inserted: 22 jan 2013
Last Updated: 17 jun 2013

Journal: M3AS
Year: 2013


In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $\Gamma$-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.