Dirichlet problem associated with a random quasilinear operator in a random domain
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996) no. 1, p. 103-121
@article{M2AN_1996__30_1_103_0,
     author = {Abddaimi, Y. and Michaille, G\'erard},
     title = {Dirichlet problem associated with a random quasilinear operator in a random domain},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {30},
     number = {1},
     year = {1996},
     pages = {103-121},
     zbl = {0881.35010},
     mrnumber = {1378613},
     language = {en},
     url = {http://http://www.numdam.org/item/M2AN_1996__30_1_103_0}
}
Abddaimi, Y.; Michaille, G. Dirichlet problem associated with a random quasilinear operator in a random domain. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996) no. 1, pp. 103-121. http://www.numdam.org/item/M2AN_1996__30_1_103_0/

[1] M. A. Ackoglu, U. Krengel, 1981, Ergodic Theorems for Superadditive Processes, J. Reine. Ang. Math., 323, pp. 53-67. | MR 611442 | Zbl 0453.60039

[2] H. Attouch, 1984, Variational Convergence for functions and operators, Research Notes in Mathematics, Pitman, London. | MR 773850 | Zbl 0561.49012

[3] J. P. Aubin-H. Frankowska, 1990, Set Valued Analysis, Birkhäuser. | MR 1048347 | Zbl 0713.49021

[4] M. Balzano, 1988, Random perfored Dirichlet problems, Ann. Mat. Para Appl. (4), 153. | MR 1008342 | Zbl 0673.60067

[5] A. Bensoussan, 1989, Homogenization with random oscillating coefficients, Partial differential Equations and the Calculus of Variation, Vol. I, Essays in the Honor of E. De Giorgi, F. Colombini, A. Marino, L. Modica, S. Spagnolo Editors, Birkhäuser. | MR 1034003 | Zbl 0686.60056

[6] L. Boccardo, F. Murat, J. P. Puel, 1984, Résultats d'existence pour certains problèmes elliptiques quasilinéaires, Ann. Scuola Norm. Sup. Pisa, cl. Sci. (4) 11, pp. 213-235. | Numdam | MR 764943 | Zbl 0557.35051

[7] A. Bourgeat, A. Mikelic, S. Wright, 1994, Stochastic Two-scale Convergence in the mean and applications, J. Für die Reine angew. Math., 456, pp, 19-51. | MR 1301450 | Zbl 0808.60056

[8] A. Brillard, 1990, Homogénéisation de quelques équations de la mécanique des milieux continus. Thèse d'état.

[9] C. Castaing, M. Valadier, 1977, Convex Analysis and Measurable Multifunctions, Lect. Notes in Math., vol. 580, Springer Verlag. | MR 467310 | Zbl 0346.46038

[10] E. Chabi, G. Michaille, 1995, Random Dirichlet problem : scalar Darcy law, Potential Analysis, vol. 4, 2, pp. 119-140. | MR 1323822 | Zbl 0821.60029

[11] E. Chabi, Homogénéisation stochastique et théorie ergodique, Thèse d'État soutenue le 25 mai 1993, Université Moulay Ismail, Faculté des Sciences, Meknès.

[12] M. Chipot, G. Michaille, 1989, Uniqueness result and monotonicity properties for strongly nonlinear elliptic variational inequalities, Ann. Scuola Norm. Sup. Pisa, cl. Sci., vol. XVI, 1, pp. 137-166. | Numdam | MR 1056131 | Zbl 0699.35113

[13] J. L. Lions, 1981, Some Methods in the Mathematical Analysis of Systems and Their Control, Science Press, Gordon and Breach. | MR 664760 | Zbl 0542.93034

[14] G. Dal-Maso, A. Garroni, 1993, A new approach to the study of limits of Dirichlet problems in perforated domains, Preprint S.I.S.A. 67/M (May).

[15] G. Dal Maso, L. Modica, 1986, Nonlinear Stochastic Homogenization and Ergodic Theory, J. Reine Angew. Math., 368, pp. 28-42. | MR 850613 | Zbl 0582.60034

[16] S. M. Koslov, 1980, Averraging of random operators, Math. USSR. Sbornik, 37, pp. 167-180. | Zbl 0444.60047

[17] U. Krengel, 1985, Ergodic Theorems, Walter de Gruyter, Studies in Math. | MR 797411 | Zbl 0575.28009

[18] G. C. Papanicolaou, 1985, Macroscopic properties of composites, bubby fluids, suspensions and related problems, Les méthodes de l'homogénéisation : théorie et applications en physique, CEA-EDF INRIA, École d'été d'analyse numérique, Eyrolles. | MR 844872

[19] K. Sab, 1992, On the homogenization and simulation of random materials, European Journal of Mechanics, A/Solids, 11, 5. | MR 1184222 | Zbl 0766.73008