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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Zhang, Guoqing¹  Geng, Xiaoqian¹ 

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

关键词: Isoperimetric problem;    Power-law potentials;    Minimizers;   

DOI  :  10.1016/j.jmaa.2019.123521

来源: Elsevier

【 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.

【 授权许可】

Free