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.
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 = {http://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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