On the isoperimetric problem with double density
Abstract
In this paper we consider the isoperimetric problem with double density in an Euclidean space, that is, we study the minimisation of the perimeter among subsets of with fixed volume, where volume and perimeter are relative to two different densities. The case of a single density, or equivalently, when the two densities coincide, has been well studied in the last years; nonetheless, the problem with two different densities is an important generalisation, also in view of applications. We will prove the existence of isoperimetric sets in this context, extending the known results for the case of single density.
Cite
@article{arxiv.1804.02966,
title = {On the isoperimetric problem with double density},
author = {Aldo Pratelli and Giorgio Saracco},
journal= {arXiv preprint arXiv:1804.02966},
year = {2018}
}
Comments
19 pages, 1 figure. A subscript $r$ is missing in the hypothesis of Theorem A and related Lemmas in the published version. This version contains the correct statements