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 1932961 | Zbl 1065.35045 | 1 citation dans Numdam

DOI : https://doi.org/10.1051/cocv:2002048
Classification : 35B27, 35A25, 42C30
Mots clés : homogenization, Bloch waves, correctors, regularity, spectral problems, vibration problems

@article{COCV_2002__8__489_0,
     author = {Conca, Carlos and Vanninathan, M.},
     title = {Fourier approach to homogenization problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {489--511},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     doi = {10.1051/cocv:2002048},
     zbl = {1065.35045},
     mrnumber = {1932961},
     language = {en},
     url = {www.numdam.org/item/COCV_2002__8__489_0/}
}

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://www.numdam.org/item/COCV_2002__8__489_0/

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