The regularity and Neumann problem for non-symmetric elliptic operators

We establish optimal L^p bounds for the nontangential maximal function of the gradient of the solution to a second order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the vertical variable, on the domain above a Lipschitz graph in the plane, in terms of the L^p norm at the boundary of the tangential derivative of the Dirichlet data, or of the Neumann data.