The Lp Dirichlet problem for second order elliptic operators and a p-adapted square function

We establish Lp-solvability for 1 < p <∞ of the Dirichlet problem on Lipschitz domains with small Lipschitz constants for elliptic divergence and non-divergence type operators with rough coefficients obeying a certain Carleson condition with small norm. © 2006 Published by Elsevier Inc.