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

2024/11/12 by Dipierro, Serena, Valdinoci, Enrico, Villa, Riccardo · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.07727

Abstract

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.

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• Γ-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations

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