$\Gamma$-convergence of convolution-type functionals for free discontinuity problems
Analysis of PDEs
2026-03-26 v1 Optimization and Control
Abstract
We prove compactness with respect to -convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free discontinuity functionals defined on the space of generalised special functions of bounded variation. We then characterise the bulk and surface energy densities of the obtained limits by means of minimisation problems on small cubes for the approximating energies.
Cite
@article{arxiv.2603.24192,
title = {$\Gamma$-convergence of convolution-type functionals for free discontinuity problems},
author = {Giuseppe Cosma Brusca and Davide Donati and Sergio Scalabrino and Chiara Trifone and Edoardo Voglino},
journal= {arXiv preprint arXiv:2603.24192},
year = {2026}
}
Comments
38 pages