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.
Bellettini, G., Chambolle, A., Goldman, M. (2014). The Gamma-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 24(6), 1091-1113 [10.1142/S0218202513500772].
The Gamma-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension
BELLETTINI, GIOVANNI;
2014-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
