Document Zbl 1375.35264

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

Adv. Differ. Equ. 21, No. 7-8, 631-698 (2016).

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.

Cited in 14 Documents

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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