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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.

##### MSC:
 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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