JournalsjemsVol. 13, No. 5pp. 1477–1503

Homogenization in polygonal domains

  • David Gérard-Varet

    Ecole Normale Superieure, Paris, France
  • Nader Masmoudi

    New York University, USA
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Abstract

We consider the homogenization of elliptic systems with \eps\eps-periodic coefficients. Classical two-scale approximation yields a O(\eps)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.

Cite this article

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

DOI 10.4171/JEMS/286