paper

Quantitative analysis of boundary layers in periodic homogenization

arXiv:1607.06716 · doi:10.1007/s00205-017-1142-z

Abstract

We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition.

41 pages; updated to comment on results of arXiv:1610.05273

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