Homogenization of a parabolic Dirichlet problem by a method of Dahlberg

Alejandro J. Castro, Martin Strömqvist

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)439-473
Number of pages35
JournalPublicacions Matematiques
Volume62
Issue number2
DOIs
Publication statusPublished - Jan 1 2018

Keywords

  • Dirichlet problem
  • Homogenization
  • Second order parabolic operator

ASJC Scopus subject areas

  • Mathematics(all)

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