Convergence of the Allen-Cahn equation to multi-phase mean-curvature flow

  • Tim Laux (MPI MiS, Leipzig)
A3 01 (Sophus-Lie room)


We present a convergence result for solutions of the vector-valued Allen-Cahn equation. In the spirit of the work of Luckhaus and Sturzenhecker we establish convergence towards a distributional formulation of multi-phase mean-curvature flow using sets of finite perimeter. Like their result, ours relies on the assumption that the time-integrated energies of the approximations converge to those of the limit.

This is joint work with Thilo Simon (MPI MIS).

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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