Fourier approach to homogenization problems

Conca, Carlos; Vanninathan, M.

doi:10.1051/cocv:2002048

Conca, Carlos ; Vanninathan, M.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 489-511.

Résumé

This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic structures.

MR Zbl | 1 citation dans Numdam

DOI : 10.1051/cocv:2002048

Classification : 35B27, 35A25, 42C30
Mots-clés : homogenization, Bloch waves, correctors, regularity, spectral problems, vibration problems

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Conca, Carlos; Vanninathan, M. Fourier approach to homogenization problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 489-511. doi : 10.1051/cocv:2002048. http://archive.numdam.org/articles/10.1051/cocv:2002048/

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