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Article type: Research Article
Authors: Josien, Marc; *
Affiliations: CERMICS, École des Ponts, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France. E-mail: marc.josien@mis.mpg.de
Correspondence: [*] Corresponding author. E-mail: marc.josien@mis.mpg.de.
Abstract: This article is about the Zd-periodic Green function Gn(x,y) of the multiscale elliptic operator Lu=−div(A(n·)·∇u), where A(x) is a Zd-periodic, coercive, and Hölder continuous matrix, and n is a large integer. We prove here pointwise estimates on Gn(x,y), ∇xGn(x,y), ∇yGn(x,y) and ∇x∇yGn(x,y) in dimensions d⩾2. Moreover, we derive an explicit decomposition of this Green function, which is of independent interest. These results also apply for systems.
Keywords: Green function, periodic homogenization, multiscale problems
DOI: 10.3233/ASY-181504
Journal: Asymptotic Analysis, vol. 112, no. 3-4, pp. 227-246, 2019
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