Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

An Lq(Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx , which, in particular, contains all measurable functions depending only on t . The method of proving simplifies the methods previously used in the case p = q. © 2007 Elsevier Inc. All rights reserved.