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