Symmetry problem

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Symmetry problem - publisher's PDF.pdf (156.92 KB)

Date

Authors

Ramm, Alexander G.

Abstract

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier: if Δu = 1 in D ⊂ R[superscript 3], u = 0 on S, the boundary of D, and u[subscript 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.

Keywords

Symmetry, Symmetry problems, Pompeiu problem

URI

http://hdl.handle.net/2097/15212

Collections

Mathematics Faculty Research and Publications

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