| Issue |
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
|
|
|---|---|---|
| Page(s) | 489 - 511 | |
| DOI | https://doi.org/10.1051/cocv:2002048 | |
| Published online | 15 August 2002 | |
Fourier approach to homogenization problems
1
Departamento de Ingeniería
Matemática, and Centro de Modelamiento Matemático,
Universidad de Chile, Casilla 170/3, Correo-3, Santiago, Chile; cconca@dim.uchile.cl.
2
IISc-TIFR
Mathematics Programme, TIFR Centre, P.O. Box 1234, Bangalore
560 012, India; vanni@math.tifrbng.res.in.
Received:
14
January
2002
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.
Mathematics Subject Classification: 35B27 / 35A25 / 42C30
Key words: Homogenization / Bloch waves / correctors / regularity / spectral problems / vibration problems.
© EDP Sciences, SMAI, 2002
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