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This article is part of the series Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations.

Open Access Open Badges 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

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/030190

Received:3 June 2006
Accepted:21 September 2006
Published:30 November 2006

© 2007 Lewis and Vogel

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.

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.


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