Elliptic equations with discontinuous coefficients in generalized Morrey spaces

We make a further step in the study of regularizing properties of the strong solutions to the equation [Equation not available: see fulltext.]where Ω is a bounded domain in Rn with smooth boundary. We are interested in estimating the second order derivatives of the solutions and in showing that solutions belong to the class C1,α. The relevant assumptions on the leading coefficients are uniform ellipticity and their membership to the class L∞∩ VMO. Moreover, the assumptions on the lower order term are optimal in the sense that they are assumed to belong to some generalized Morrey classes.