Numerical approximation of positive power curvature flow via deterministic games
This provides a novel game-theoretic numerical method for a specific class of curvature flows, which is incremental for experts in geometric PDEs.
The authors approximate the level set solution for curvature flow with speed max(0, κ)^γ (1/3<γ<1) using deterministic two-person games, proving convergence to the viscosity solution and proposing a numerical scheme.
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.