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Symmetry Theorems and Uniform Rectifiability

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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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Keywords

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