Fourier approach to homogenization problems

Carlos Conca; M. Vanninathan

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 8, page 489-511
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Conca, Carlos, and Vanninathan, M.. "Fourier approach to homogenization problems." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 489-511. <http://eudml.org/doc/90658>.

@article{Conca2010,
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. },
author = {Conca, Carlos, Vanninathan, M.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Homogenization; Bloch waves; correctors; regularity; spectral problems; vibration problems.; regularity; vibration problems; elliptic operators},
language = {eng},
month = {3},
pages = {489-511},
publisher = {EDP Sciences},
title = {Fourier approach to homogenization problems},
url = {http://eudml.org/doc/90658},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Conca, Carlos
AU - Vanninathan, M.
TI - Fourier approach to homogenization problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 489
EP - 511
AB - 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.
LA - eng
KW - Homogenization; Bloch waves; correctors; regularity; spectral problems; vibration problems.; regularity; vibration problems; elliptic operators
UR - http://eudml.org/doc/90658
ER -

References

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