Regularity for entropy solutions of parabolic p-Laplacian type equations

In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut - div ap(x, [del] u)= f in ]0,T[x [omega] with initial datum in L 1 ([omega]) and assuming Dirichlet's boundary condition, where ap(., .) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f [member] L 1 (]0,T[x [omega]) and [omega] is a domain in R N. We find spaces of type L r (0,T ; M q ([omega])) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian equation is considered