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  • Research Article
  • Open Access

Symmetry Theorems and Uniform Rectifiability

Boundary Value Problems20062007:030190

https://doi.org/10.1155/2007/30190

  • Received: 3 June 2006
  • Accepted: 21 September 2006
  • Published:

Abstract

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.

Keywords

  • Boundary Condition
  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation

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Authors’ 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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