Symmetry of solutions to some systems of integral equations

被引：95
作者：
Jin, C [1 ]
Li, CM [1 ]
机构：
[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 06期
关键词：
Hardy-Littlewood-Sobolev inequalities; systems of integral equations; radial symmetry; classification of solution;
D O I：
10.1090/S0002-9939-05-08411-X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study some systems of integral equations, including those related to Hardy-Littlewood-Sobolev (HLS) inequalities. We prove that, under some integrability conditions, the positive regular solutions to the systems are radially symmetric and monotone about some point. In particular, we established the radial symmetry of the solutions to the Euler-Lagrange equations associated with the classical and weighted Hardy-Littlewood-Sobolev inequality.
引用
收藏
页码：1661 / 1670
页数：10
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