Homogenization and boundary layer

@inproceedings{GrardVaret2010HomogenizationAB,
  title={Homogenization and boundary layer},
  author={David G{\'e}rard-Varet and Nader Masmoudi},
  year={2010}
}
This paper deals with the homogenization of elliptic systems with Dirichlet boundary condition, when the coefficients of both the system and the boundary data are ε-periodic. We show that, as ε → 0, the solutions converge in L2 with a power rate in ε, and identify the homogenized limit system. Due to a boundary layer phenomenon, this homogenized system depends in a non trivial way on the boundary. Our analysis answers a longstanding open problem, raised for instance in [7]. It extends… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 28 references

Compactness methods in the theory of homogenization

  • Marco Avellaneda, Fang-Hua Lin
  • Comm. Pure Appl. Math.,
  • 1987
Highly Influential
9 Excerpts

Asymptotic analysis for periodic structures, volume 5 of Studies in Mathematics and its Applications

  • Alain Bensoussan, Jacques-Louis Lions, George Papanicolaou
  • 1978
Highly Influential
5 Excerpts

Relevance of the slip condition for fluid flows near an irregular boundary

  • David Gérard-Varet, Nader Masmoudi
  • Comm. Math. Phys.,
  • 2010
1 Excerpt

The general theory of homogenization, volume 7 of Lecture Notes of the Unione Matematica Italiana

  • Luc Tartar
  • 2009
1 Excerpt

Homogenization, volume 234 of Translations of Mathematical Monographs

  • G. A. Chechkin, A. L. Piatnitski, A. S. Shamaev
  • American Mathematical Society, Providence, RI,
  • 2007
1 Excerpt

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