Accepted Paper

Inserted: 10 nov 2023
Last Updated: 19 jun 2025

Journal: J. Funct. Anal.
Year: 2025
Doi: https://doi.org/10.1016/j.jfa.2025.111106

Abstract:

We consider a family of non-local and non-convex functionals, and we prove that their Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total variation. As a by-product, we answer some open questions concerning the limiting behavior of these functionals. The proof relies on the analysis of a discretized version of these functionals.