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vibration problems.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Fourier approach to homogenization problems
Carlos Conca, M. Vanninathan
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 8 / 2002

Published online by Cambridge University Press:

15 August 2002, pp. 489-511

Print publication:

2002
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This article is divided into two chapters. Theclassical problem of homogenization of elliptic operators withperiodically oscillating coefficients is revisited in thefirst chapter. Following a Fourier approach, we discuss someof 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 isdevoted to the discussion of some non-classical behaviour ofvibration problems of periodic structures.