Advances in Differential Equations

A level set crystalline mean curvature flow of surfaces

Yoshikazu Giga and Norbert Požár

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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.

Article information

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

Dates
First available in Project Euclid: 3 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ade/1462298654

Mathematical Reviews number (MathSciNet)
MR3493931

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

Citation

Giga, Yoshikazu; Požár, Norbert. A level set crystalline mean curvature flow of surfaces. Adv. Differential Equations 21 (2016), no. 7/8, 631--698. https://projecteuclid.org/euclid.ade/1462298654.


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