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.
"A level set crystalline mean curvature flow of surfaces." Adv. Differential Equations 21 (7/8) 631 - 698, July/August 2016.