A level-set method for a mean curvature flow with a prescribed boundary

DOI HANDLE Open Access

Abstract

We propose a level-set method for a mean curvature flow whose boundary is prescribed by interpreting the boundary as an obstacle. Since the corresponding obstacle problem is globally solvable, our method gives a global-in-time level-set mean curvature flow under a prescribed boundary with no restriction of the profile of an initial hypersurface. We show that our solution agrees with a classical mean curvature flow under the Dirichlet condition. We moreover prove that our solution agrees with a level-set flow under the Dirichlet condition constructed by P. Sternberg and W. P. Ziemer (1994), where the initial hypersurface is contained in a strictly mean-convex domain and the prescribed boundary is on the boundary of the domain.

Journal

Keywords

Details 詳細情報について

  • CRID
    1390578141487603968
  • DOI
    10.14943/107831
  • HANDLE
    2115/90094
  • Text Lang
    en
  • Data Source
    • JaLC
    • IRDB
  • Abstract License Flag
    Allowed

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