Symmetry problem

Author:
A. G. Ramm

Journal:
Proc. Amer. Math. Soc. **141** (2013), 515-521

MSC (2010):
Primary 35J05, 31B20

DOI:
https://doi.org/10.1090/S0002-9939-2012-11400-5

Published electronically:
May 31, 2012

MathSciNet review:
2996955

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier: if in , on , the boundary of , and on , then is a sphere. It is assumed that is a Lipschitz surface homeomorphic to a sphere. This result has been proved in different ways by various authors. Our proof is based on a simple new idea.

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Additional Information

**A. G. Ramm**

Affiliation:
Department of Mathematics, Kansas State University, Manhattan, Kansas 66506-2602

Email:
ramm@math.ksu.edu

DOI:
https://doi.org/10.1090/S0002-9939-2012-11400-5

Keywords:
Symmetry problems,
potential theory.

Received by editor(s):
December 6, 2010

Received by editor(s) in revised form:
June 25, 2011

Published electronically:
May 31, 2012

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2012
American Mathematical Society

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