Consider the linear parabolic operator in divergence form [Equation presented here]. 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.
- Dirichlet problem
- Second order parabolic operator
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