Rothe's Method for Parabolic Problems with Nonlinear Degenerating Coeecient

In the paper we investigate local existence of a weak solution u to a degenerate parabolic boundary value problem. Degeneration occurs in the coeecient g(x; t; u) in front of the time derivative which is not assumed to be bounded below by some positive constant. Moreover, this coeecient depends on the solution u. We approximate the problem by semidiscretization in time (Rothe's method) and prove uniform convergence of the approximations to a HH older continuous weak solution. The assumptions with respect to u for the nonlinear coeecient and the right-hand side are supposed only in a neighbourhood of the initial function, therefore we have to derive a L 1-estimate for the approximates. This estimate that implies also HH older continuity is obtained by a Moser technique.