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Regularity of a free boundary problem

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Abstract

Let u be the Newtonian potential of a real analytic distribution in an open set Ω. In this paper we assume u is analytically continuable from the complement of Ω into some neighborhood of a point x0 ∈ ∂Ω, and we study conditions under which the analytic continuation implies that ∂Ω is a real analytic hypersurface in some neighborhood of x0.

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Authors and Affiliations

  1. Department of Applied Mathematics, Ort Braude College Campus, P.O. box 78, 20101, Carmiel, Israel

    Lavi Karp

  2. Department of Mathematics, Technion - Israel Institute of Technology, 32000, Haifa, Israel

    Lavi Karp

  3. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Henrik Shahgholian

Authors
  1. Lavi Karp
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  2. Henrik Shahgholian
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Correspondence to Lavi Karp.

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Communicated by Steven Krantz

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Karp, L., Shahgholian, H. Regularity of a free boundary problem. J Geom Anal 9, 653–669 (1999). https://doi.org/10.1007/BF02921977

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  • DOI: https://doi.org/10.1007/BF02921977

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