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.
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.
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@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 = {https://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 - https://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 https://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, Volume 339 (2004) no. 1, pp. 77-82. doi : 10.1016/j.crma.2004.03.028. https://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
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