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

2015/11/05 by Keisuke Takasao, Takasao, Keisuke · 1 citation
Mathematics · #35K93 #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35K93 #msc:53C44

paper · pdf · doi:10.48550/arxiv.1511.01687

16 pages

arxiv created 2015/11/05 · arxiv updated 2015/11/06

Abstract

We study the phase field method for the volume preserving mean curvature flow. Given an initial C¹ 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.

Cited by

• Varifold solutions to Volume-Preserving Mean Curvature Flow: existence and weak-strong uniqueness

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