Existence of Weak Solution for Volume Preserving Mean Curvature Flow via Phase Field Method
نویسندگان
چکیده
Abstract. 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.
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تاریخ انتشار 2016