Symmetry of solutions to some systems of integral equations

Authors:
Chao Jin and Congming Li

Journal:
Proc. Amer. Math. Soc. **134** (2006), 1661-1670

MSC (2000):
Primary 35J99, 45E10, 45G05

DOI:
https://doi.org/10.1090/S0002-9939-05-08411-X

Published electronically:
October 28, 2005

MathSciNet review:
2204277

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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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Additional Information

**Chao Jin**

Affiliation:
Department of Applied Mathematics, Campus Box 526, University of Colorado at Boulder, Boulder, Colorado 80309

Email:
jinc@colorado.edu

**Congming Li**

Affiliation:
Department of Applied Mathematics, Campus Box 526, University of Colorado at Boulder, Boulder, Colorado 80309

Email:
cli@colorado.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-08411-X

Keywords:
Hardy-Littlewood-Sobolev inequalities,
systems of integral equations,
radial symmetry,
classification of solution

Received by editor(s):
July 28, 2004

Received by editor(s) in revised form:
December 29, 2004

Published electronically:
October 28, 2005

Additional Notes:
This work was partially supported by NSF grant DMS-0401174.

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.