Consider the linear parabolic operator in divergence form Hu=∂tu(X,t)−div(A(X)∇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 Lp, for any elliptic matrix of
coefficients A which is periodic and satisfies a Dini-type condition. This
result allows us to treat a homogenization problem for the equation ∂tuε(X,t)−div(A(X/ε)∇uε(X,t)) in
Lipschitz domains with Lp-boundary data.Comment: 21 page