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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David Gérard-Varet, Nader Masmoudi, Homogenization in polygonal domains. J. Eur. Math. Soc. 13 (2011), no. 5, pp. 1477–1503DOI 10.4171/JEMS/286