Symmetry problem
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Abstract:
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier: if $\Delta u=1$ in $D\subset \mathbb {R}^3$, $u=0$ on $S$, the boundary of $D$, and $u_N=const$ on $S$, then $S$ is a sphere. It is assumed that $S$ 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.References
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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
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2996955