Calculus of Variations and Geometric Measure Theory

V. Scattaglia

A formula for the minimal perimeter of clusters with density

created by scattaglia on 08 Dec 2020



Inserted: 8 dec 2020
Last Updated: 8 dec 2020

Year: 2020


This paper deals with the isoperimetric problem for clusters in a Euclidean space with double density. In particular, we show that a limit of an isoperimetric minimizing sequence of clusters with volumes V is always isoperimetric for its own volumes (which may be smaller than V). In particular, if it is strictly smaller, we provide an explicit formula.

Keywords: isoperimetric problem, Clusters, Weighted measure