The Cauchy-Dirichlet problem for parabolic equations with VMO coefficients

In this note, we prove the well posedness for a Cauchy-Dirichlet problem in the class W-p(1,2), for every p between 1 and infinity. The main part of the linear parabolic operator is symmetric, uniformly elliptic and belongs to the Sarason's class VMO. Consequently, we prove a boundary estimate of the solution u, where the related constant depends on coefficients only through the ellipticity constant and the VMO moduli. (c) 2005 Elsevier Ltd. All rights reserved.