The ε - εβ Property in the Isoperimetric Problem with Double Density, and the Regularity of Isoperimetric Sets

Abstract

We prove the validity of the ε-εβ{\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

• isoperimetric problem
• anisotropic perimeter
• finsler surface energy
• boundedness
• regularity
• 49q10
• 49q20
• 58b20