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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.

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