The $\epsilon -{\epsilon }^{\beta }$ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets

Abstract

We prove the validity of the $\epsilon -{\epsilon }^{\beta }$ property in the isoperimetric problem with double density, generalising the known properties for the case of single density. As a consequence, we derive regularity for isoperimetric sets.

19 pages, 1 figure