Gradient estimates in generalized Morrey spaces for parabolic operators

We obtain global regularity in generalized Morrey spaces for the gradient of the weak solutions to divergence form linear parabolic operators with measurable data. Assuming partial BMO smallness of the coefficients and Reifenberg flatness of the boundary of the underlying domain, we develop a Calderón-Zygmund type theory for such operators. Problems like the considered here arise in the modeling of composite materials and in the mechanics of membranes and films of simple nonhomogeneous materials which form a linear laminated medium.