Recent progress in the theory of homogenization with oscillating Dirichlet data
Analysis of PDEs
2013-01-31 v1
Abstract
This note is a summary of the recent paper [9]. Here, we study the homogenization of elliptic systems with Dirichlet boundary condition, when both the coefficients and the boundary datum are oscillating. In particular, in the paper [9], we showed that, the solutions converge in L2 with a power rate, and we identified the homogenized limit system and the homogenized boundary data. Due to a boundary layer phenomenon, this homogenized system depends in a non trivial way on the boundary. The analysis in [9] answers a longstanding open problem, raised for instance in [4]
Cite
@article{arxiv.1301.7229,
title = {Recent progress in the theory of homogenization with oscillating Dirichlet data},
author = {David Gerard-Varet and Nader Masmoudi},
journal= {arXiv preprint arXiv:1301.7229},
year = {2013}
}