Advances in Differential Equations
- Adv. Differential Equations
- Volume 21, Number 7/8 (2016), 631-698.
A level set crystalline mean curvature flow of surfaces
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.
Adv. Differential Equations Volume 21, Number 7/8 (2016), 631-698.
First available in Project Euclid: 3 May 2016
Permanent link to this document
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. https://projecteuclid.org/euclid.ade/1462298654