Calculus of Variations and Geometric Measure Theory

M. Gobbino - N. Picenni

Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms

created by picenni on 10 Nov 2023



Inserted: 10 nov 2023

Year: 2023

ArXiv: 2311.05560 PDF


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.