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Homogenization and boundary layers. (English) Zbl 1259.35024
This paper considers a linear elliptic system with periodically oscillating coefficients in the PDE system as well as in the Dirichlet boundary data. The authors perform a fine boundary layer analysis and are able to identify as \(\epsilon\) (the periodicity parameter) goes to zero a set of “homogenized” equations as well as an \(L^2\)-corrector estimate for the oscillating (weak) solutions. This generalizes the authors previous results on the same mathematical question to the case of more general domains.

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J58 Boundary value problems for higher-order elliptic systems
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