Explicit viscosity solution of the crystalline curvature flow with fattening (Geometric aspects of solutions to partial differential equations)

Abstract

We give a simple explicit example of a solution of the level set formulation of the crystalline curvature flow in two dimensions whose one level set fattens, leading to nonuniqueness of the flow, and prove that it is the unique viscosity solution. The motivation of this note is to illustrate the notion of viscosity solutions introduced recently by Y. Giga and the author.