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Boundary Value Problems
Boundary Value Problems Cover Image
  • Research Article
  • Open Access

Symmetry Theorems and Uniform Rectifiability

Boundary Value Problems20062007:030190

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

©  J. L. Lewis and A. L. Vogel 2007

  • 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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Copyright

© J. L. Lewis and A. L. Vogel 2007

This article is published under license to BioMed Central Ltd. 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.

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