Homogenization and boundary layers. (English) Zbl 1259.35024

Gérard-Varet, David; Masmoudi, Nader

Acta Math. 209, No. 1, 133-178 (2012).

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.

Reviewer: Adrian Muntean (Eindhoven)

MSC:

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

Keywords:

oscillating Dirichlet data; boundary layers; \(L^2\)-corrector estimate