Solvability of parabolic equations in divergence form with partially BMO coefficients

We prove the H1p solvability of second order parabolic equations in divergence form with leading coefficients aij measurable in (t, x1) and having small BMO (bounded mean oscillation) semi-norms in the other variables. Additionally we assume a11 is measurable in x1 and has small BMO semi-norms in the other variables. The corresponding results for the Cauchy problem are also established. Parabolic equations in Sobolev spaces H1 q,p with mixed norms are also considered under the same conditions of the coefficients. © 2010 Elsevier Inc. All rights reserved