Existence and almost everywhere regularity of isoperimetric clusters for fractional perimeters

TL;DR

This paper proves the existence of minimizers and establishes partial regularity results for isoperimetric clusters involving fractional perimeters, advancing understanding of their geometric and regularity properties.

Contribution

It introduces new existence and regularity results for fractional isoperimetric clusters with multiple volume constraints.

Findings

Existence of minimizers for fractional isoperimetric problems.

Partial regularity of the minimizers.

Advancement in understanding fractional perimeter geometric properties.

Abstract

The existence of minimizers in the fractional isoperimetric problem with multiple volume constraints is proved, together with a partial regularity result.