Global-Local subadditive ergodic theorems and application to homogenization in elasticity
Licht, Christian ; Michaille, Gérard
Annales mathématiques Blaise Pascal, Tome 9 (2002), p. 21-62 / Harvested from Numdam
Publié le : 2002-01-01
@article{AMBP_2002__9_1_21_0,
     author = {Licht, Christian and Michaille, G\'erard},
     title = {Global-Local subadditive ergodic theorems and application to homogenization in elasticity},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {9},
     year = {2002},
     pages = {21-62},
     mrnumber = {1914260},
     zbl = {01805820},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2002__9_1_21_0}
}
Licht, Christian; Michaille, Gérard. Global-Local subadditive ergodic theorems and application to homogenization in elasticity. Annales mathématiques Blaise Pascal, Tome 9 (2002) pp. 21-62. http://gdmltest.u-ga.fr/item/AMBP_2002__9_1_21_0/

[1] Y. Abddaimi. Homogénéisation de quelques problèmes en analyse variationnelle, application des théorèmes ergodiques sous-additifs. Thèse, Univerité Montpellier 2, 1996.

[2] Y. Abddaimi, C. Licht, and G. Michaille. Stochastic homogenization for an integral functional of quasiconvex function with linear growth. Asymptotic Analysis, 15:183-202, 1997. | MR 1480998 | Zbl 0912.49013

[3] M.A. Ackoglu and U. Krengel. Ergodic theorems for superadditive processes. J. Reine angew. Math., 323:53-67, 1981. | MR 611442 | Zbl 0453.60039

[4] H. Attouch. Variational Convergence for Functions and Operators. Pitman Advanced Publishing Program, London, 1985. | MR 773850 | Zbl 0561.49012

[5] H. Attouch and R J.B. Wets. Epigraphical processes : laws of large numbers for random lsc functions. Séminaire d'Analyse Convexe, 13, 1990. | MR 1114683 | Zbl 0744.60021

[6] M. Bellieud and G. Bouchitté. Homogenization of elliptic problems in a fiber reinforced structure. Ann. Scuola Norm. Sup. Pisa, Serie IV, XXVI, 4, 1998. | Numdam | MR 1635769 | Zbl 0919.35014

[7] G. Bouchitté, I. Fonseca, and L. Mascarenhas. A global method for relaxation. Arch. Rational Mech. Anal., 145:51-98, 1998. | MR 1656477 | Zbl 0921.49004

[8] A. Braides. Homogenization of some almost-periodic functional. Rend. Accad. Naz. XL, 103:313-322, 1985. | MR 899255 | Zbl 0582.49014

[9] B. Dacorogna. Direct methods in the Calculus of Variations. Springer-Verlag, Berlin, 1989. | MR 990890 | Zbl 0703.49001

[10] C. Hess. Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator. The Annals of Statistics, 24:1298-1315, 1996. | MR 1401851 | Zbl 0862.62029

[11] U. Krengel. Ergodic Theorems. Walter de Gruyter, Berlin, New York, 1985. | MR 797411 | Zbl 0575.28009

[12] C. Licht and G. Michaille. Une modélisation du comportement d'un joint collé élastique. C.R. Acad. Sci. Paris, 322, Série I:295-300, 1996. | MR 1378271 | Zbl 0863.73019

[13] C. Licht and G. Michaille. A modelling of elastic adhesive bonding joints. Mathematical Sciences and Applications, 7:711-740, 1997. | MR 1476274 | Zbl 0892.73007

[14] G. Dal Masoand L. Modica. Non linear stochastic homogenization and ergodic theory. J. Reine angew. Math., 363:27-43, 1986. | MR 850613 | Zbl 0582.60034

[15] G. Michaille, J. Michel, and L. Piccinini. Large deviations estimates for epigraphical superadditive processes in stochastic homogenization. prepublication ENS Lyon, 220, 1998.

[16] S. Muller. Homogenization of non convex integral functionals and cellular elastic material. Arch. Rational Mech. Anal., 7:189-212, 1987. | Zbl 0629.73009

[17] R.T. Rockafellar. Integral functionals, normal integrands and measurable selections. Lecture Notes in Mathematics, 543:133-158, 1979. | MR 512209 | Zbl 0374.49001

[18] Nguyen Xuhan Xanhand H. Zessin. Ergodic theorems for spatial processes. Z. Wah. Verw. Gebiete, 48:133-158, 1979. | MR 534841 | Zbl 0397.60080