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.
Gobbino, M., Picenni, N. (2025). Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms. JOURNAL OF FUNCTIONAL ANALYSIS, 289(10) [10.1016/j.jfa.2025.111106].
Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms
Picenni, Nicola
2025-01-01
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.File in questo prodotto:
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