WIAS Preprint No. 2054, (2014)

Overdetermined problems for the fractional Laplacian in exterior and annular sets



Authors

  • Soave, Nicola
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35N25 35R11 35A02

Keywords

  • Rigidity and classification results, fractional Laplacian, unbounded domains, overdetermined problems

Abstract

We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are necessarily radially symmetric. The extension of the result in bounded non-convex regions is also studied, as well as the radial symmetry of the solution when the set is a priori supposed to be rotationally symmetric.

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