Homogenization of a parabolic Dirichlet problem by a method of Dahlberg

• Autores: Alejandro J. Castro, Martin Strömqvist
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 62, Nº 2, 2018, págs. 439-473
• Idioma: inglés
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• Resumen

  • 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.