Numerical approximation of positive power curvature flow via deterministic games

Abstract

We approximate the level set solution for the motion of an embedded closed curve in the plane with normal speed $\max(0, κ)^{\ga}$ where $κ$ is the curvature of the curve and $\frac{1}{3}<\ga<1$ by the value functions of a family of deterministic two person games. We show convergence of the value functions to the viscosity solution of the level set equation and propose a numerical scheme for the calculation of the value function.