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Homogenization of a parabolic Dirichlet problem by a method of Dahlberg
Castro, Alejandro J. (Nazarbayev University (Astana, Kazakhstan). Department of Mathematics)
Strömqvist, Martin (Uppsala University. Department of Mathematics)

Data: 2018
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: Article ; recerca ; Versió publicada
Matèria: Second order parabolic operator ; Dirichlet problem ; Homogenization
Publicat a: Publicacions matemàtiques, Vol. 62 Núm. 2 (2018) , p. 439-473 (Articles) , ISSN 2014-4350

Adreça original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/338219
DOI: 10.5565/PUBLMAT6221805


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