Homogenization of a parabolic Dirichlet problem by a method of Dahlberg

Consider the linear parabolic operator in divergence form: Hu := partial derivative(t)u (X, t) - div(A (X) del u (X, t)). We employ a method of Dahlberg to show that the Dirichlet problem for H in the upper half plane is well-posed for boundary data in L-p, for any elliptic matrix of coef-ficients A which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation partial derivative(t)u(epsilon) (X, t) - div(A (X/epsilon) del u(epsilon) (X, t)) in Lipschitz domains with L-p-boundary data