Symmetry of minimizers for some nonlocal variational problems

被引：21

作者：

Lopes, Orlando ^{[2
]}

Maris, Mihai ^{[1
]}

机构：

[1] Univ Franche Comte, Dept Math, UMR 6623, F-25030 Besancon, France

[2] IMEUSP, BR-05315970 Sao Paulo, Brazil

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2008年 / 254卷 / 02期

关键词：

symmetry of minimizers; nonlocal functional; minimization under constraints; fractional powers of Laplacian; Choquard functional; Davey-Stewartson equation;

D O I：

10.1016/j.jfa.2007.10.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a new approach to study the symmetry of minimizers for a large class of nonlocal variational problems. This approach which generalizes the Reflection method is based on the existence of some integral identities. We study the identities that lead to symmetry results, the functionals that can be considered and the function spaces that can be used. Then we use our method to prove the symmetry of minimizers for a class of variational problems involving the fractional powers of Laplacian, for the generalized Choquard functional and for the standing waves of the Davey-Stewartson equation. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：535 / 592

页数：58

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