Homogenization of a Parabolic Dirichlet Problem by a Method of Dahlberg
نویسنده
چکیده
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 forH 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.
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تاریخ انتشار 2018