Symmetry of solutions to some systems of integral equations

Jin, Chao; Li, Congming

doi:10.1090/S0002-9939-05-08411-X

Symmetry of solutions to some systems of integral equations
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by Chao Jin and Congming Li PDF

Proc. Amer. Math. Soc. 134 (2006), 1661-1670 Request permission

Abstract:

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.

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