On non-local almost minimal sets and an application to the non-local Massari's Problem

Fuente: arXiv
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Autori principali: Dipierro, Serena, Valdinoci, Enrico, Villa, Riccardo
Natura: Preprint
Pubblicazione: 2024
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author Dipierro, Serena
Valdinoci, Enrico
Villa, Riccardo
author_facet Dipierro, Serena
Valdinoci, Enrico
Villa, Riccardo
contents We consider a fractional Plateau's problem dealing with sets with prescribed non-local mean curvature. This problem can be seen as a non-local counterpart of the classical Massari's Problem. We obtain existence and regularity results, relying on a suitable version of the non-local theory for almost minimal sets. In this framework, the fractional curvature term in the energy functional can be interpreted as a perturbation of the fractional perimeter. In addition, we also discuss stickiness phenomena for non-local almost minimal sets.
format Preprint
id arxiv_https___arxiv_org_abs_2411_07727
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On non-local almost minimal sets and an application to the non-local Massari's Problem
Dipierro, Serena
Valdinoci, Enrico
Villa, Riccardo
Analysis of PDEs
We consider a fractional Plateau's problem dealing with sets with prescribed non-local mean curvature. This problem can be seen as a non-local counterpart of the classical Massari's Problem. We obtain existence and regularity results, relying on a suitable version of the non-local theory for almost minimal sets. In this framework, the fractional curvature term in the energy functional can be interpreted as a perturbation of the fractional perimeter. In addition, we also discuss stickiness phenomena for non-local almost minimal sets.
title On non-local almost minimal sets and an application to the non-local Massari's Problem
topic Analysis of PDEs
url https://arxiv.org/abs/2411.07727