The best constant in a weighted Hardy-Littlewood-Sobolev inequality

Authors:
Wenxiong Chen and Congming Li

Journal:
Proc. Amer. Math. Soc. **136** (2008), 955-962

MSC (2000):
Primary 35J45, 35J60; Secondary 45G05, 45G15

DOI:
https://doi.org/10.1090/S0002-9939-07-09232-5

Published electronically:
November 30, 2007

MathSciNet review:
2361869

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the uniqueness for the solutions of the singular nonlinear PDE system:

(1) |

In the special case when and , we classify all the solutions and thus obtain the best constant in the corresponding weighted Hardy-Littlewood-Sobolev inequality.

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Additional Information

**Wenxiong Chen**

Affiliation:
College of Mathematics and Information Science, Henan Normal University, People’s Republic of China

Address at time of publication:
Department of Mathematics, Yeshiva University, 500 W. 185th Street, New York, New York 10033

Email:
wchen@yu.edu

**Congming Li**

Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309

Email:
cli@colorado.edu

DOI:
https://doi.org/10.1090/S0002-9939-07-09232-5

Keywords:
Weighted Hardy-Littlewood-Sobolev inequality,
best constants,
system of singular PDEs,
uniqueness,
radial symmetry,
classifications

Received by editor(s):
November 13, 2006

Published electronically:
November 30, 2007

Additional Notes:
The first author was partially supported by NSF Grant DMS-0604638

The second author was partially supported by NSF Grant DMS-0401174

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2007
American Mathematical Society

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