On non-local almost minimal sets and an application to the non-local Massari's Problem
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.
Fields of Study & Subjects
Fixed Point Theorems Analysis
Optimization and Variational Analysis
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Journal de Mathématiques Pures et Appliquées
- Publisher
- Elsevier BV
- Volume
- 208
- Pages
- 103840–103840
- Publication date
- 5 January 2026
- Language
- EN