SINGULAR DEGENERATE PARABOLIC EQUATIONS WITH APPLICATIONS TO THE P-LAPLACE DIFFUSION EQUATION

We consider singular degenerate parabolic equations including the p-la place diffusion equation. We establish a comparison principle which is a natural extension of the paper [13] by Ishii and Souganidis. Once w e get a comparison principle we can construct the unique global-in-tim e viscosity solution to the Cauchy problem for the p-laplace diffusion equation. The solution is bounded, uniformly continuous in [O, T) x R -N if the initial data is bounded, uniformly continuous on R-N.