Inserted: 14 oct 2019
Last Updated: 30 jul 2020
Journal: Adv. Nonlinear Stud.
We prove the validity of the $\varepsilon-\varepsilon^\beta$ 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.
Keywords: regularity, anisotropic perimeter, isoperimetric problem, Finsler surface energy, boundedness, $\varepsilon-\varepsilon$ property