The inverse mean curvature flow as an obstacle problem

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Abstract

The inverse mean curvature flow is a geometric evolution problem that is turned into a degenerate elliptic problem by a level set formulation. In the latter form, it may be regarded as a special case of an obstacle problem. In this paper, solutions of the problem are constructed with an approximation by p-harmonic functions and the use of appropriate barrier functions. This also extends the known existence results for weak solutions of the inverse mean curvature flow.
Original languageEnglish
Pages (from-to)2235-2256
Number of pages22
JournalIndiana University Mathematics Journal
Volume57
Issue number5
DOIs
Publication statusPublished - 2008

Keywords

  • p-harmonic
  • inverse mean curvature flow
  • obstacle problem

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