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Symmetry of solutions to some systems of integral equations
Author(s):
Chao
Jin;
Congming
Li
Journal:
Proc. Amer. Math. Soc.
134
(2006),
1661-1670.
MSC (2000):
Primary 35J99, 45E10, 45G05
Posted:
October 28, 2005
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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:
10.1090/S0002-9939-05-08411-X
PII:
S 0002-9939(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
Posted:
October 28, 2005
Additional Notes:
This work was partially supported by NSF grant DMS-0401174.
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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