A semi-Lagrangian scheme for the game $p$-Laplacian via $p$-averaging

Abstract

We present and analyze an approximation scheme for the two-dimensional game $p$-Laplacian in the framework of viscosity solutions. The approximation is based on a semi-Lagrangian scheme which exploits the idea of $p$-averages. We study the properties of the scheme and prove that it converges, in particular cases, to the viscosity solution of the game $p$-Laplacian. We also present a numerical implementation of the scheme for different values of $p$; the numerical tests show that the scheme is accurate.

34 pages, 3 figures. To appear on Applied Numerical Mathematics

Cited by in corpus (1)

• A natural approach to the asymptotic mean value property for the $p$-Laplacian