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Symmetry Theorems and Uniform Rectifiability

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.

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Correspondence to John L Lewis.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Lewis, J.L., Vogel, A.L. Symmetry Theorems and Uniform Rectifiability. Bound Value Probl 2007, 030190 (2006). https://doi.org/10.1155/2007/30190

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Keywords

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