On an isoperimetric problem with power-law potentials and external attraction

摘要

In this paper, an isoperimetric problem with power-law potentials and external attraction is considered. Using concentration-compactness lemma for sets of finite perimeter which was introduced by Frank and Lieb, we prove the existence of minimizers for the isoperimetric problem. In the special case of quadratic attraction, we also obtain that the ball is the unique minimizer of the isoperimetric problem. (C) 2019 Elsevier Inc. All rights reserved.