Open Access
2018 Homogenization of a parabolic Dirichlet problem by a method of Dahlberg
Alejandro J. Castro, Martin Strömqvist
Publ. Mat. 62(2): 439-473 (2018). DOI: 10.5565/PUBLMAT6221805


Consider the linear parabolic operator in divergence form $$ \mathcal{H} u :=\partial_t u(X,t)-\operatorname{div}(A(X)\nabla u(X,t)). $$ We employ a method of Dahlberg to show that the Dirichlet problem for $\mathcal{H}$ in the upper half plane is well-posed for boundary data in $L^p$, 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 $\partial_t u_\varepsilon(X,t)-\operatorname{div}(A(X/\varepsilon)\nabla u_\varepsilon(X,t))$ in Lipschitz domains with $L^p$-boundary data.


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Alejandro J. Castro. Martin Strömqvist. "Homogenization of a parabolic Dirichlet problem by a method of Dahlberg." Publ. Mat. 62 (2) 439 - 473, 2018.


Received: 9 January 2017; Published: 2018
First available in Project Euclid: 16 June 2018

zbMATH: 1393.35077
MathSciNet: MR3815286
Digital Object Identifier: 10.5565/PUBLMAT6221805

Primary: 35B27 , 35K20

Keywords: Dirichlet problem , Homogenization‎ , Second order parabolic operator

Rights: Copyright © 2018 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.62 • No. 2 • 2018
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