Generalized Money estimates for the gradient of divergence form parabolic operators with discontinuous coefficients

Abstract

We consider the Cauchy Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg-flat domains. The coefficients are supposed to be only measurable in one of the space variables and small BMO with respect to the others. We obtain boundedness of the Hardy-Littlewood maximal operator in the generalized Morrey spaces W-rho,W-phi, p is an element of (1, infinity) and weight phi satisfying certain supremum condition. This permits us to obtain Calderon-Zygmund type estimate for the gradient of the weak solution of the problem. (C) 2015 Elsevier Inc. All rights reserved.