Summability of Solutions of Elliptic and Parabolic Quasilinear Equations with Measures as Data

We give a result of summability of solution of elliptic and parabolic boundary and initial-boundary value problems associated with an operator of Leray-Lions type when the right-hand side and the initial condition are two bounded Radon measures. This work generalizes the results of papers by L. Boccardo and T. Gallouet [J. Convex Analysis 3 (1996) 361–365] and Li Feng-Quan and Li Guang-Wei [J. Convex Analysis 7 (2000) 203–208].