Symmetry of solutions to some systems of integral equations
Symmetry of solutions to some systems of integral equations
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DOI：
10.1090/s0002-9939-05-08411-x
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发表时间：
2005-10
期刊：
影响因子：
--
通讯作者：
Chaosong Jin;Congming Li
中科院分区：
文献类型：
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作者：
Chaosong Jin;Congming Li
在本文中，我们研究了一些积分方程组，包括与 Hardy-Littlewood-Sobolev (HLS) 不等式相关的方程组。我们证明，在某些可积条件下，系统的正则解是径向对称的并且关于某个点单调。特别是，我们建立了与经典和加权 Hardy-Littlewood-Sobolev 不等式相关的欧拉-拉格朗日方程解的径向对称性。
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.