A level set crystalline mean curvature flow of surfaces

2016/01/08 by Yoshikazu Giga, Giga, Yoshikazu, Norbert Požár +1 · 2 citations
Mathematics · #35B51 #35D40 #35K55 #35K67 #35K93 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B51 #msc:35D40 #msc:35K55 #msc:35K67 #msc:35K93

paper · pdf · doi:10.48550/arxiv.1601.01802

55 pages, 4 figures

arxiv created 2016/01/08 · arxiv updated 2016/01/11

Abstract

We introduce a new notion of viscosity solutions for the level set formulation of the motion by crystalline mean curvature in three dimensions. The solutions satisfy the comparison principle, stability with respect to an approximation by regularized problems, and we also show the uniqueness and existence of a level set flow for bounded crystals.

Cited by

• Variational Nonlinear and Nonlocal Curvature Flows
• A distributional approach to nonlocal curvature flows

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