Open Access

Symmetry Theorems and Uniform Rectifiability

Boundary Value Problems20062007:030190

DOI: 10.1155/2007/30190

Received: 3 June 2006

Accepted: 21 September 2006

Published: 30 November 2006

Abstract

We study overdetermined boundary conditions for positive solutions to some elliptic partial differential equations of https://static-content.springer.com/image/art%3A10.1155%2F2007%2F30190/MediaObjects/13661_2006_Article_641_IEq1_HTML.gif -Laplacian type in a bounded domain https://static-content.springer.com/image/art%3A10.1155%2F2007%2F30190/MediaObjects/13661_2006_Article_641_IEq2_HTML.gif . We show that these conditions imply uniform rectifiability of https://static-content.springer.com/image/art%3A10.1155%2F2007%2F30190/MediaObjects/13661_2006_Article_641_IEq3_HTML.gif and also that they yield the solution to certain symmetry problems.

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Authors’ Affiliations

(1)
Department of Mathematics, University of Kentucky
(2)
Department of Mathematics, Syracuse University

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Copyright

© J. L. Lewis and A. L. Vogel 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.