@article{AIHPC_1997__14_5_669_0,
author = {Casado-D{\'\i}az, Juan},
title = {Homogenization of a quasi-linear problem with quadratic growth in perforated domains : an example},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {669--686},
publisher = {Gauthier-Villars},
volume = {14},
number = {5},
year = {1997},
mrnumber = {1470785},
zbl = {0942.35051},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1997__14_5_669_0/}
}
TY - JOUR AU - Casado-Díaz, Juan TI - Homogenization of a quasi-linear problem with quadratic growth in perforated domains : an example JO - Annales de l'I.H.P. Analyse non linéaire PY - 1997 SP - 669 EP - 686 VL - 14 IS - 5 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_1997__14_5_669_0/ LA - en ID - AIHPC_1997__14_5_669_0 ER -
%0 Journal Article %A Casado-Díaz, Juan %T Homogenization of a quasi-linear problem with quadratic growth in perforated domains : an example %J Annales de l'I.H.P. Analyse non linéaire %D 1997 %P 669-686 %V 14 %N 5 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPC_1997__14_5_669_0/ %G en %F AIHPC_1997__14_5_669_0
Casado-Díaz, Juan. Homogenization of a quasi-linear problem with quadratic growth in perforated domains : an example. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) no. 5, pp. 669-686. http://www.numdam.org/item/AIHPC_1997__14_5_669_0/
[1] and , Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions. Arch. Rat. Mech. Anal., Vol. 133, 1, 1995, pp. 77-101. | MR | Zbl
[2] , and , H-Convergence for quasilinear elliptic equations with quadratic growth, Appl. Math. Optim., Vol. 26, 3, 1992, pp. 253-272. | MR | Zbl
[3] , , and , H-convergence for quasilinear elliptic equations under natural hypotheses on the correctors. In Composite Media and Homogenization Theory II (Proceedings, Trieste, September 1993), ed. by G. DAL MASO, G. F. DELL'ANTONIO, 1995, World Scientific, Singapore, pp. 93-112.
[4] , and , Existence de solutions faibles pour des équations elliptiques quasi-linéaires à croissance quadratique. In Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. IV, ed. by H. BRÉZIS, J.-L. LIONS. Research Notes in Math., Vol. 84, 1983, Pitman, London, pp. 19-73. | MR | Zbl
[5] , Sobre la homogeneización de problemas no coercivos y problemas en dominios con agujeros. Ph. D. Thesis, University of Seville, 1993.
[6] , Homogenization of general quasi-linear Dirichlet problems with quadratic growth in perforated domains. To appear in J. Math. Pur. App. | MR | Zbl
[7] , Homogenization of Dirichlet problems for monotone operators in varying domains. To appear in P. Roy. Soc. Edimburgh. | MR | Zbl
[8] and , Asymptotic behaviour of Dirichlet solutions of nonlinear elliptic systems in varying domains. To appear.
[9] and , Un terme étrange venu d'ailleurs. In Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. II and III, ed. by H. BRÉZIS, J.-L. LIONS. Research Notes in Math. Vol. 60 and 70, 1982, Pitman, London, pp. 98-138 and pp. 154-178. | Zbl
[10] and , New results on the asymptotic behaviour of Dirichlet problems in perforated domains, Math. Mod. Meth. Appl. Sci., Vol. 3, 1994, pp. 373-407. | MR | Zbl
[11] and , Wiener criterion and Γ - convergence. Appl. Math. Optim. Vol. 15 1987, pp. 15-63. | MR | Zbl
[12] and , Wiener-criteria and energy decay for relaxed Dirichlet problems. Arch. Rat. Mech. Anal., Vol. 95, 4, 1986, pp. 345-387. | MR | Zbl
[13] and , Dirichlet problems in perforated domains for homogeneous monotone operators on H10. In Calculus of Variations, Homogenization and Continuum Mechanics (Proceedings, Cirm-Lumigny, Marseille, June 21-25, 1993), ed. by G. Bouchitté, G. Buttazzo, P. Suquet. Series on Advances in Mathematics for Applied Sciences 18, World Scientific, Singapore, 1994, pp. 177-202. | MR | Zbl
[14] and , Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. To appear. | Numdam | MR | Zbl
[15] and , Measure theory and fine properties of functions. Studies in Advanced Mathematics., CRC Press, Boca Raton, 1992. | MR | Zbl
[16] and , The Lebesgue set of a function whose distribution derivatives are p-th power summable. Indiana U. Math. J., Vol. 22, 1972, 139-158. | MR | Zbl
[17] , and , Quasilinear relaxed Dirichlet problems. Siam J. Math. Anal., Vol. 27, 4, 1996, pp. 977-996. | MR | Zbl
[18] and , Corrector results for relaxed Dirichlet problems. Asymptotic Analysis, Vol. 5, 1992, pp. 269-281. | MR | Zbl
[19] and , Estimation de l'erreur dans des problèmes de Dirichlet où apparaît un terme étrange. In Partial Differential Equations and the Calculus of Variations, Vol. II, Essays in honor of E. De Giorgi, ed. by F. Colombini, L. Modica, A. Marino, S. Spagnolo. Progress in Nonlinear Differential Equations and their Applications 2, Birkhäuser, Boston, 1989, pp. 661-696. | MR | Zbl
[20] , An Lp estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Sc. Norm. Sup. Pisa C. Sci., Vol. 3, 17, 1963, pp. 189-206. | Numdam | MR | Zbl
[21] , H-convergence.Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger 1977/1978, mimeographed notes. English translation: F. MURAT, L. TARTAR, H-convergence. In Mathematical Modelling of Composites Materials, ed. by R. V. KOHN. Progress in Nonlinear Differential Equations and their Applications, Birkhäuser, Boston. To appear.
[22] , Homogenization of renormalized solutions of elliptic equations. Ann. Inst. H. Poincaré, Anal. non linéaire, Vol. 8, 1991, pp. 309-332. | Numdam | MR | Zbl
[23] , Weakly differentiable functions. Springer-Verlag, New York, 1989. | MR | Zbl
