Inserted: 22 jan 2013
Last Updated: 17 jun 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.