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Symmetry Theorems and Uniform Rectifiability

Boundary Value Problems volume 2007, Article number: 030190 (2006) Cite this article

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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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506-0027, USA

    John L Lewis

  2. Department of Mathematics, Syracuse University, Syracuse, NY, 13244, USA

    Andrew L Vogel

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  1. John L Lewis
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  2. Andrew L Vogel
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Correspondence to John L Lewis.

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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