Existence of isoperimetric sets with densities "converging from below" in ${\mathbb{R}}^N$

Guido De Philippis, Giovanni Franzina, Aldo Pratelli

In this paper, we consider the isoperimetric problem in the space ${\mathbb{R}}^N$ with density. Our result states that, if the density f is l.s.c. and converges to a positive limit…