THE FIRST BOUNDARY VALUE PROBLEM FOR STRONGLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS IN ANISOTROPIC SOBOLEV SPACES*

This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.