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arXiv · 2301.12237

Convergence of Allen-Cahn equations to De Giorgi's multiphase mean curvature flow

Pascal Steinke
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Abstract

This paper presents a conditional convergence result of solutions to the Allen--Cahn equation with arbitrary potentials to a De Giorgi type $ \mathrm{BV} $-solution to multiphase mean curvature flow. Moreover we show that De Giorgi type $\mathrm{BV} $-solutions are De Giorgi type varifold solutions, and thus our solution is unique in a weak-strong sense.

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Pascal Steinke. 2023-01-28. Convergence of Allen-Cahn equations to De Giorgi's multiphase mean curvature flow. https://arxiv.org/abs/2301.12237

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