We propose a technique to treat degenerate elliptic equations, focusing on the model problem of the stationary Mean Curvature Motion equation in two space dimensions. This technique may be interpreted as a stationary, fully discrete version of the schemes proposed in slightly different forms by Catte ́ et al. and by Kohn and Serfaty. We study consistency and monotonicity of the scheme and a correct implementation of Dirichlet boundary conditions. Numerical tests are also presented.
Carlini, E., Ferretti, R. (2008). A Semi-Lagrangian approximation of min-max type for the stationary Mean Curvature equation. In Numerical Mathematics and Advanced Applications - ENUMATH 2007 (pp.679-686).