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Open Access Research Article

Symmetry Theorems and Uniform Rectifiability

John Lewis1* and Andrew L Vogel2

Author Affiliations

1 Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA

2 Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA

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Boundary Value Problems 2007, 2007:030190  doi:10.1155/2007/30190

Published: 30 November 2006

Abstract

We study overdetermined boundary conditions for positive solutions to some elliptic partial differential equations of -Laplacian type in a bounded domain . We show that these conditions imply uniform rectifiability of and also that they yield the solution to certain symmetry problems.