Accepted Paper

Inserted: 13 jan 2026
Last Updated: 13 jan 2026

Journal: Journal de Mathématiques Pures et Appliquées
Year: 2024

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.