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