Existence of weak solution for volume preserving mean curvature flow via phase field method

Keisuke Takasao

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arXiv · 1511.01687

Existence of weak solution for volume preserving mean curvature flow via phase field method

Keisuke Takasao

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Abstract

We study the phase field method for the volume preserving mean curvature flow. Given an initial $C^1$ hypersurface we proved the existence of the weak solution for the volume preserving mean curvature flow via the reaction diffusion equation with a nonlocal term. We also show the monotonicity formula and the density upper bound for the reaction diffusion equation.

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Keisuke Takasao. 2015-11-05. Existence of weak solution for volume preserving mean curvature flow via phase field method. https://arxiv.org/abs/1511.01687

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