%0 Journal Article
%T 两个相位的非局部等周问题的基态解的存在性<br>Existence of Ground States Solutions for a Nonlocal Isoperimetric Problem with Two Phases
%A 黄帅飞
%J Advances in Applied Mathematics
%P 2719-2729
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.115288
%X 本文主要研究了具有幂律势的两个相位的非局部等周问题。利用集中紧性原理，证明了具有两个相位的非局部等周问题基态解的存在性。本文是在泛函的极小值的存在性的背景下，研究了两个相位的非局部等周问题的基态解的存在性，主要运用集中紧性方法，证明了紧性成立，从而证明基态解的存在性。<br />
A nonlocal isoperimetric problem of two phases with power-law potentials is investigated. Using the concentration-compactness lemma, we prove the existence of ground states for the nonlocal isop-erimetric problem with two phases. In this paper, the existence of the ground state solution of the nonlocal isoperimetric problem with two phases is investigated in the context of the existence of the minimal value of the generalized function, and the existence of the ground state solution is proved by proving that the compactness holds, using the method of concentration-compactness lemma.
%K 非局部等周问题，基态，幂律势<br>Nonlocal Isoperimetric Problem
%K Ground States
%K Power-Low Potentials
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=51609