On obstacle problem for Brakke's mean curvature flow

2021/02/12 by Takasao, Keisuke · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35K93 #Secondary 53E10

paper · doi:10.48550/arxiv.2102.06375

Abstract

We consider the obstacle problem of the weak solution for the mean curvature flow, in the sense of Brakke's mean curvature flow. We prove the global existence of the weak solution with obstacles which have C^1,1 boundaries, in two and three space dimensions. To obtain the weak solution, we use the Allen-Cahn equation with forcing term.

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• Generic mean curvature flow with obstacles

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