@article{ASNSP_1997_4_24_2_239_0,
author = {Dal Maso, Gianni and Murat, Fran\c{c}ois},
title = {Asymptotic behaviour and correctors for {Dirichlet} problems in perforated domains with homogeneous monotone operators},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {239--290},
year = {1997},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 24},
number = {2},
mrnumber = {1487956},
zbl = {0899.35007},
language = {en},
url = {https://www.numdam.org/item/ASNSP_1997_4_24_2_239_0/}
}
TY - JOUR AU - Dal Maso, Gianni AU - Murat, François TI - Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1997 SP - 239 EP - 290 VL - 24 IS - 2 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_1997_4_24_2_239_0/ LA - en ID - ASNSP_1997_4_24_2_239_0 ER -
%0 Journal Article %A Dal Maso, Gianni %A Murat, François %T Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1997 %P 239-290 %V 24 %N 2 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_1997_4_24_2_239_0/ %G en %F ASNSP_1997_4_24_2_239_0
Dal Maso, Gianni; Murat, François. Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 24 (1997) no. 2, pp. 239-290. https://www.numdam.org/item/ASNSP_1997_4_24_2_239_0/
[1] , Variational Convergence for Functions and Operators., Pitman, London, 1984. | Zbl
[2] - , Variational inequalities with varying obstacles: the general form of the limit problem, J. Funct. Anal. 50 (1983), 329-386.
[3] , Quasi topologies and rational approximation, J. Funct. Anal. 10 (1972), 259-268. | Zbl
[4] - , Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal. 19 (1992), 581-597. | Zbl
[5] - , Shape optimizationforDirichletproblems: relaxed solutions and optimality conditions, Appl. Math. Optim. 23 (1991), 17-49. | Zbl
[6] - - , A derivation theorem for capacities with respect to a Radon measure, J. Funct. Anal. 71 (1987), 263-278. | Zbl
[7] - - , Asymptotic behaviour for Dirichlet problems in domains bounded by thin layers, Partial Differential Equations and the Calculus of Variations, Essays in Honor of Ennio De Giorgi, 193-249, Birkhäuser, Boston, 1989. | Zbl
[8] , Homogenization of a quasi-linear problem with quadratic growth in perforated domains: an example, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. | Zbl | Numdam
[9] , Homogenization of general quasi-linear problems with quadratic growth in perforated domains, J. Math. Pures Appl., to appear. | Zbl
[10] , Homogenization of Dirichlet problems for monotone operators in varying domains, Proc. Roy. Soc. Edinburgh Sect. A, to appear. | Zbl
[11] , Existence of a sequence satisfying Cioranescu-Murat conditions in homogenization of Dirichlet problems in perforated domains, Rend. Mat., to appear. | Zbl
[12] - , Asymptotic behaviour of nonlinear elliptic systems on varying domains, to appear. | Zbl
[13] - , Relaxed shape optimization: the case of nonnegative data for the Dirichlet problem, Adv. Math. Sci. Appl. 1 (1992), 47-81. | Zbl
[14] - , Un terme étrange venu d'ailleurs, I and II. Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar. Vol. II, 98-138, and Vol. III, 154-178, Res. Notes in Math., 60 and 70, Pitman, London, 1982 and 1983. English translation: A strange term coming from nowhere. Topics in the Mathematical Modelling of Composite Materials, Birkhäuser, Boston, to appear. | Zbl
[15] , Limits of minimum problems for general integralfunctionals with unilateral obstacles, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 74 (1983), 55-61. | Zbl
[16] , On the integral representation of certain local functionals, Ricerche Mat. 32 (1983), 85-113. | Zbl
[17] , r-convergence and μ-capacities,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987), 423-464. | Zbl | Numdam
[18] , An Introduction to Γ-Convergence, Birkhäuser, Boston, 1993. | Zbl
[19] - , Some properties of a class of nonlinear variational μ-capacities, J. Funct. Anal. 79 (1988), 476-492. | Zbl
[20] - , Limits of nonlinear Dirichlet problems in varying domains, Manuscripta Math. 61 (1988), 251-278. | Zbl
[21] - , New results on the asymptotic behaviour of Dirichlet problems in perforated domains, Math. Mod. Meth. Appl. Sci. 3 (1994), 373-407. | Zbl
[22] - , Approximation of relaxed Dirichlet problems by boundary value problems in perforated domains, Proc. Roy. Soc. Edinburgh Sect. A 124 (1995), 99-114. | Zbl
[23] - , Wiener criteria and energy decay for relaxed Dirichlet problems, Arch. Rational Mech. Anal. 95 (1986), 345-387. | Zbl
[24] - , Wiener's criterion and r-convergence, Appl. Math. Optim. 15 (1987), 15-63. | Zbl
[25] - , Dirichlet problems in perforated domains for homogeneous monotone operators on H10, Calculus of Variations, Homogenization and Continuum Mechanics (CIRM-Luminy, Marseille, 1993), 177-202, World Scientific, Singapore, 1994. | Zbl
[26] - , Asymptotic behaviour of nonlinear Dirichlet problems in perforated domains, Ann. Mat. Pura Appl., to appear. | Zbl
[27] - , Limits of minimum problems with convex obstacles for vector valued functions, Applicable Anal. 52 (1994), 1-33. | Zbl
[28] , Measure Theory, Van Nostrand, Princeton, 1950. | Zbl
[29] , Non-linear potentials and approximation in the mean by analytic functions, Math. Z. 129 (1972), 299-319. | Zbl
[30] - - , Nonlinear Potential Theory of Degenerate Elliptic Equations, Clarendon Press, Oxford, 1993. | Zbl
[31] , The method of orthogonal projections and the Dirichlet problems in domains with a fine-grained boundary, Math. USSR-Sb. 17 (1972), 37-59. | Zbl
[32] , On G-convergence of operators of Dirichlet problem with varying domain, Dokl. Akad. Nauk Ukrain. Ser. A 5 (1993), 13-17. | Zbl
[33] - , Homogenization of nonlinear Dirichlet problem in a periodically perforated domain, Recent Advances in Nonlinear Elliptic and Parabolic Problems (Nancy, 1988), 294-305, Res. Notes in Math. 208, Longman, Harlow, 1989. | Zbl
[34] - , Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. | Zbl
[35] , Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris, 1969. | Zbl
[36] - , Existence and regularity results for relaxed Dirichlet problems with measure data, Ann. Mat. Pura Appl., to appear. | Zbl
[37] - , Boundary Value Problems in Domains with Fine-Granulated Boundaries (in Russian), Naukova Dumka, Kiev, 1974. | Zbl
[38] - , Error estimate for the homogenization of a quasilinear Dirichlet problem in a periodically perfored domain, Progress in Partial Differential Equations: the Metz Survey 2, 185-193, Pitman Res. Notes in Math. 296, Longman, New York, 1993. | Zbl
[39] , Asymptotic behaviour of Dirichlet problems on a Riemannian manifold, Ricerche Mat. 41 (1992), 327-367. | Zbl
[40] , Nonlinear Elliptic Boundary Value Problems, Teubner-Verlag, Leipzig, 1986. | Zbl
[41] , Methods for Analysis of Nonlinear Elliptic Boundary Value Problems (in Russian), Nauka, Moscow, 1990. English translation in: Translations of Mathematical Monographs 139, American Mathematical Society, Providence, 1994. | Zbl
[42] , Averaging nonlinear Dirichlet problems in domains with channels, Soviet Math. Dokl. 42 (1991), 853-857. | Zbl
[43] , Asymptotic behaviour of solutions of nonlinear elliptic problems in perforated domains, Mat. Sb. (N.S.) 184 (1993), 67-90. | Zbl
[44] , Homogenization of nonlinear Dirichlet problems in perforated domains of general structure, Mat. Sb. (N.S.) 187 (1996), 125-157. | Zbl
[45] , New conditions for the homogenization of nonlinear Dirichlet problems in perforated domains, Ukrain. Mat. Zh., to appear. | Zbl
[46] , Cours Peccot au Collège de France Paris, 1977, partially written in: : H-convergence. Séminaire d'Analyse Fonctionnelle et Numérique, Université d'Alger, 1977-78. English translation: , : H-convergence. Topics in the Mathematical Modelling of Composite Materials, Birkhäuser, Boston, to appear.
[47] , Weakly Differentiable Functions, Springer-Verlag, Berlin, 1989. | Zbl






