Journal of the European Mathematical Society

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Volume 13, Issue 5, 2011, pp. 1477–1503
DOI: 10.4171/JEMS/286

Published online: 2011-07-13

Homogenization in polygonal domains

David Gérard-Varet[1] and Nader Masmoudi[2]

(1) Ecole Normale Superieure, Paris, France
(2) New York University, USA

We consider the homogenization of elliptic systems with $\eps$-periodic coefficients. Classical two-scale approximation yields a $O(\eps)$ error inside the domain. We discuss here the existence of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis extends substantially previous results obtained for polygonal domains with sides of rational slopes.

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Gérard-Varet David, Masmoudi Nader: Homogenization in polygonal domains. J. Eur. Math. Soc. 13 (2011), 1477-1503. doi: 10.4171/JEMS/286