An integral equation on half space

Authors:
Dongyan Li and Ran Zhuo

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2779-2791

MSC (2010):
Primary 35J99, 45E10, 45G05

Published electronically:
April 14, 2010

MathSciNet review:
2644892

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the -dimensional upper half Euclidean space, and let be any real number satisfying In this paper, we consider the integral equation

where , and is the reflection of the point about the hyperplane . We use a new type of moving plane method in integral forms introduced by Chen, Li and Ou to establish the regularity and rotational symmetry of the solution of the above integral equation.

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Additional Information

**Dongyan Li**

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

Email:
w408867388w@126.com

**Ran Zhuo**

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

Email:
zhuoran1986@126.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-10-10368-2

Keywords:
Integral equations,
regularity,
method of moving planes,
rotational symmetry,
upper half space,
monotonicity.

Received by editor(s):
September 25, 2009

Published electronically:
April 14, 2010

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2010
American Mathematical Society

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