Symmetry Theorems and Uniform Rectifiability
1 Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA
2 Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA
Boundary Value Problems 2007, 2007:030190 doi:10.1155/2007/30190Published: 30 November 2006
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.