Existence of Weak Solution for Volume-Preserving Mean Curvature Flow via Phase Field Method

We study the phase field method for the volume-preserving mean curvature flow. Given an initial data which is a measure-theoretic boundary of a Caccioppoli set with a suitable density bound, we prove the existence of the weak solution for the volume-preserving mean curvature flow via the reaction di...

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Bibliographic Details
Published in:Indiana University mathematics journal 2017-01, Vol.66 (6), p.2015-2035
Main Author: Takasao, Keisuke
Format: Article
Language:English
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Summary:We study the phase field method for the volume-preserving mean curvature flow. Given an initial data which is a measure-theoretic boundary of a Caccioppoli set with a suitable density bound, we prove 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 for the reaction diffusion equation.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2017.66.6183