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

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Parabolic Problems
Homogenization
Dirichlet Problem
Parabolic Operator
Lipschitz Domains
Half-plane
Linear Operator
Divergence
Coefficient
Form

Keywords

  • Dirichlet problem
  • Homogenization
  • Second order parabolic operator

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Homogenization of a parabolic Dirichlet problem by a method of Dahlberg. / Castro, Alejandro J.; Strömqvist, Martin.

In: Publicacions Matematiques, Vol. 62, No. 2, 01.01.2018, p. 439-473.

Research output: Contribution to journalArticle

Castro, Alejandro J. ; Strömqvist, Martin. / Homogenization of a parabolic Dirichlet problem by a method of Dahlberg. In: Publicacions Matematiques. 2018 ; Vol. 62, No. 2. pp. 439-473.
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