Boundary Layers in Periodic Homogenization

This talk is concerned with a family of elliptic systems in divergence form with rapidly oscillating periodic coefficients. I will discuss recent progress on homogenization and boundary layers for Dirichlet and Neumann problems with oscillating boundary data. The problems arise naturally in the study of higher-order convergence of solutions to boundary value problems with non-oscillating data. The use of harmonic analysis techniques in obtaining sharp estimates will be highlighted

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