Advances in Differential Equations

A level set crystalline mean curvature flow of surfaces

Yoshikazu Giga and Norbert Požár

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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.

Article information

Adv. Differential Equations, Volume 21, Number 7/8 (2016), 631-698.

First available in Project Euclid: 3 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K67: Singular parabolic equations 35D40: Viscosity solutions 35K55: Nonlinear parabolic equations 35B51: Comparison principles 35K93: Quasilinear parabolic equations with mean curvature operator


Giga, Yoshikazu; Požár, Norbert. A level set crystalline mean curvature flow of surfaces. Adv. Differential Equations 21 (2016), no. 7/8, 631--698.

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