Boundary Value Problems 
Volume 2007 (2007), Article ID 30190, 59 pages
doi:10.1155/2007/30190
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

Recommended by Ugo Pietro Gianazza

Abstract

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.