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A level set crystalline mean curvature flow of surfaces. (English) Zbl 1375.35264

Summary: 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.

MSC:

35K67 Singular parabolic equations
35K55 Nonlinear parabolic equations
35B51 Comparison principles in context of PDEs
35K93 Quasilinear parabolic equations with mean curvature operator
35D40 Viscosity solutions to PDEs
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