Preprint

Inserted: 26 mar 2026
Last Updated: 16 apr 2026

Year: 2026

Abstract:

We prove compactness with respect to $Γ$-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.