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arXiv · 2311.05560

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

Massimo Gobbino·Nicola Picenni
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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.

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Massimo Gobbino, Nicola Picenni. 2023-11-09. Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms. https://arxiv.org/abs/2311.05560

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