Finite Difference Methods for the infinity Laplace and p-Laplace equations

Abstract. We build convergent discretizations and semi-implicit solvers for the Infinity Laplacian and the game theoretical p-Laplacian. The discretiza-tions simplify and generalize earlier ones. We prove convergence of the solution of the Wide Stencil finite difference schemes to the unique viscosity solution of the underlying equation. We build a semi-implicit solver, which solves the Laplace equation as each step. It is fast in the sense that the number of itera-tions is independent of the problem size. This is an improvement over previous explicit solvers, which are slow due to the CFL-condition. 1