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, ∇u) = f in ] 0,T [xΩ with initial datum in L1(Ω) and assuming Dirichlet's boundary condition, where ap(.,.) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1 (]0,T[xΩ) and Ω is a domain in RN. We find spaces of type Lr(0,T;Mq(Ω)) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian...