Boundary Value Problems
Volume 2007 (2007), Article ID 30190, 59 pages
Research Article

Symmetry Theorems and Uniform Rectifiability

John L. Lewis1 and Andrew L. Vogel2

1Department of Mathematics, University of Kentucky, Lexington 40506-0027, KY, USA
2Department of Mathematics, Syracuse University, Syracuse 13244, NY, USA

Received 3 June 2006; Accepted 21 September 2006

Academic Editor: Ugo Pietro Gianazza

Copyright © 2007 John L. Lewis and Andrew L. 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 p-Laplacian type in a bounded domain D. We show that these conditions imply uniform rectifiability of D and also that they yield the solution to certain symmetry problems.