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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Symmetry problem
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by A. G. Ramm PDF
Proc. Amer. Math. Soc. 141 (2013), 515-521 Request permission

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