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Fourier approach to homogenization problems

Published online by Cambridge University Press:  15 August 2002

Carlos Conca  and
M. Vanninathan
Carlos Conca
Affiliation:
Departamento de Ingeniería Matemática, and Centro de Modelamiento Matemático, Universidad de Chile, Casilla 170/3, Correo-3, Santiago, Chile; cconca@dim.uchile.cl.
M. Vanninathan
Affiliation:
IISc-TIFR Mathematics Programme, TIFR Centre, P.O. Box 1234, Bangalore 560 012, India; vanni@math.tifrbng.res.in.
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Abstract

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.

Keywords

HomogenizationBloch wavescorrectorsregularityspectral problemsvibration problems.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 489 - 511
Copyright
© EDP Sciences, SMAI, 2002

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