[Homogénéisation non linéaire par éclatement périodique]
Cette Note présente un résultat d'homogénéisation périodique pour des énergies intégrales à croissance polynômiale. On utilise la méthode d'éclatement périodique qui réduit la démonstration à de la convergence faible dans un espace de Lebesgue.
We consider the periodic homogenization of nonlinear integral energies with polynomial growth. The study is carried out by the periodic unfolding method which reduces the homogenization process to a weak convergence problem in a Lebesgue space.
Accepté le :
Publié le :
@article{CRMATH_2004__339_1_77_0,
author = {Cioranescu, Doina and Damlamian, Alain and De~Arcangelis, Riccardo},
title = {Homogenization of nonlinear integrals via the periodic unfolding method},
journal = {Comptes Rendus. Math\'ematique},
pages = {77--82},
publisher = {Elsevier},
volume = {339},
number = {1},
year = {2004},
doi = {10.1016/j.crma.2004.03.028},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.03.028/}
}
TY - JOUR AU - Cioranescu, Doina AU - Damlamian, Alain AU - De Arcangelis, Riccardo TI - Homogenization of nonlinear integrals via the periodic unfolding method JO - Comptes Rendus. Mathématique PY - 2004 SP - 77 EP - 82 VL - 339 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.03.028/ DO - 10.1016/j.crma.2004.03.028 LA - en ID - CRMATH_2004__339_1_77_0 ER -
%0 Journal Article %A Cioranescu, Doina %A Damlamian, Alain %A De Arcangelis, Riccardo %T Homogenization of nonlinear integrals via the periodic unfolding method %J Comptes Rendus. Mathématique %D 2004 %P 77-82 %V 339 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.03.028/ %R 10.1016/j.crma.2004.03.028 %G en %F CRMATH_2004__339_1_77_0
Cioranescu, Doina; Damlamian, Alain; De Arcangelis, Riccardo. Homogenization of nonlinear integrals via the periodic unfolding method. Comptes Rendus. Mathématique, Tome 339 (2004) no. 1, pp. 77-82. doi : 10.1016/j.crma.2004.03.028. http://www.numdam.org/articles/10.1016/j.crma.2004.03.028/
[1] Homogenization and two-scale convergence, SIAM J. Math. Anal., Volume 23 (1992), pp. 1482-1518
[2] Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal., Volume 21 (1990), pp. 823-836
[3] Homogenization: Averaging Processes in Periodic Media, Kluwer Academic, 1989
[4] Asymptotic Analysis for Periodic Structures, North-Holland, 1978
[5] Homogenization of Multiple Integrals, Oxford University Press, 1998
[6] Unbounded Functionals in the Calculus of Variations. Representation, Relaxation, and Homogenization, Chapman & Hall/CRC, 2001
[7] Some properties of Γ-limits of integral functionals, Ann. Mat. Pura Appl. (4), Volume 122 (1979), pp. 1-60
[8] An adaptation of the multi-scale methods for the analysis of bery thin reticulated structures, C. R. Acad. Sci. Paris, Sér. I Math., Volume 332 (2001), pp. 223-228
[9] Convex Analysis and Measurable Multifunctions, Lecture Notes in Math., vol. 580, Springer, 1977
[10] Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Sér. I Math., Volume 335 (2002), pp. 99-104
[11] An Introduction to Homogenization, Oxford University Press, 1999
[12] An Introduction to Γ-Convergence, Birkhäuser, 1993
[13] Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine, Boll. Un. Mat. Ital. (4), Volume 8 (1973), pp. 391-411
[14] Periodic solutions and homogenization of nonlinear variational problems, Ann. Mat. Pura Appl., Volume 4 (1978) no. 117, pp. 139-152
[15] H-Convergence (Cherkaev, A.; Kohn, R., eds.), Topics in the Mathematical Modelling of Composite Materials, Birkhäuser, 1997, pp. 21-44
[16] A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., Volume 20 (1989), pp. 608-629
Cité par Sources :
