• Corpus ID: 237453232

A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness

  title={A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness},
  author={Sebastian Hensel and Tim Laux},
We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke’s formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen’s proof [J. Differential Geom. 38, 417–461, (1993)], any limit point of solutions to the Allen–Cahn equation is a varifold solution in our… 

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