Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators
Gianni Dal Maso; François Murat
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)
- Volume: 24, Issue: 2, page 239-290
- ISSN: 0391-173X
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topDal Maso, Gianni, and 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 24.2 (1997): 239-290. <http://eudml.org/doc/84259>.
@article{DalMaso1997,
author = {Dal Maso, Gianni, Murat, François},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {monotone elliptic operators; relaxed Dirichlet problems; asymptotic behaviour},
language = {eng},
number = {2},
pages = {239-290},
publisher = {Scuola normale superiore},
title = {Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators},
url = {http://eudml.org/doc/84259},
volume = {24},
year = {1997},
}
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
PB - Scuola normale superiore
VL - 24
IS - 2
SP - 239
EP - 290
LA - eng
KW - monotone elliptic operators; relaxed Dirichlet problems; asymptotic behaviour
UR - http://eudml.org/doc/84259
ER -
References
top- [1] H. Attouch, Variational Convergence for Functions and Operators., Pitman, London, 1984. Zbl0561.49012
- [2] H. Attouch - C. Picard, Variational inequalities with varying obstacles: the general form of the limit problem, J. Funct. Anal. 50 (1983), 329-386.
- [3] T. Bagby, Quasi topologies and rational approximation, J. Funct. Anal.10 (1972), 259-268. Zbl0266.30024
- [4] L. Boccardo - F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal. 19 (1992), 581-597. Zbl0783.35020
- [5] G. Buttazzo - G. Dal Maso, Shape optimizationforDirichletproblems: relaxed solutions and optimality conditions, Appl. Math. Optim.23 (1991), 17-49. Zbl0762.49017
- [6] G. Buttazzo - G. Dal Maso - U. Mosco, A derivation theorem for capacities with respect to a Radon measure, J. Funct. Anal.71 (1987), 263-278. Zbl0622.28006
- [7] Buttazzo G. - Dal Maso G. - U. Mosco, 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. Zbl0699.35062
- [8] J. Casado Diaz, Homogenization of a quasi-linear problem with quadratic growth in perforated domains: an example, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. Zbl0942.35051
- [9] J. Casado Diaz, Homogenization of general quasi-linear problems with quadratic growth in perforated domains, J. Math. Pures Appl., to appear. Zbl0880.35015
- [10] J. Casado Diaz, Homogenization of Dirichlet problems for monotone operators in varying domains, Proc. Roy. Soc. Edinburgh Sect. A, to appear. Zbl0877.35013
- [11] J. Casado Diaz, Existence of a sequence satisfying Cioranescu-Murat conditions in homogenization of Dirichlet problems in perforated domains, Rend. Mat., to appear. Zbl0870.35013
- [12] J. Casado Diaz - A. Garroni, Asymptotic behaviour of nonlinear elliptic systems on varying domains, to appear. Zbl0952.35036
- [13] M. Chipot - G. Dal Maso, Relaxed shape optimization: the case of nonnegative data for the Dirichlet problem, Adv. Math. Sci. Appl.1 (1992), 47-81. Zbl0769.35013
- [14] D. Cioranescu - F. Murat, 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. Zbl0496.35030
- [15] G. Dal Maso, 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. Zbl0526.49006
- [16] G. Dal Maso, On the integral representation of certain local functionals, Ricerche Mat. 32 (1983), 85-113. Zbl0543.49001
- [17] G. Dal Maso, r-convergence and μ-capacities,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987), 423-464. Zbl0657.49005
- [18] G. Dal Maso, An Introduction to Γ-Convergence, Birkhäuser, Boston, 1993. Zbl0816.49001
- [19] G. Dal Maso - A. Defranceschi, Some properties of a class of nonlinear variational μ-capacities, J. Funct. Anal.79 (1988), 476-492. Zbl0657.49006
- [20] G. Dal Maso - A. Defranceschi, Limits of nonlinear Dirichlet problems in varying domains, Manuscripta Math. 61 (1988), 251-278. Zbl0653.49017
- [21] G. Dal Maso - A. Garroni, New results on the asymptotic behaviour of Dirichlet problems in perforated domains, Math. Mod. Meth. Appl. Sci. 3 (1994), 373-407. Zbl0804.47050
- [22] G. Dal Maso - A. Malusa, Approximation of relaxed Dirichlet problems by boundary value problems in perforated domains, Proc. Roy. Soc. Edinburgh Sect. A124 (1995), 99-114. Zbl0828.35007
- [23] G. Dal Maso - U. Mosco, Wiener criteria and energy decay for relaxed Dirichlet problems, Arch. Rational Mech. Anal. 95 (1986), 345-387. Zbl0634.35033
- [24] G. Dal Maso - U. Mosco, Wiener's criterion and r-convergence, Appl. Math. Optim. 15 (1987), 15-63. Zbl0644.35033
- [25] G. Dal Maso - F. Murat, 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. Zbl0884.47026
- [26] G. Dal Maso - I.V. Skrypnik, Asymptotic behaviour of nonlinear Dirichlet problems in perforated domains, Ann. Mat. Pura Appl., to appear. Zbl0991.35034
- [27] A. Defranceschi - E. Vitali, Limits of minimum problems with convex obstacles for vector valued functions, Applicable Anal. 52 (1994), 1-33. Zbl0839.49011
- [28] P.R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950. Zbl0040.16802
- [29] L.I. Hedberg, Non-linear potentials and approximation in the mean by analytic functions, Math. Z.129 (1972), 299-319. Zbl0236.31010
- [30] J. Heinonen - T. Kilpelxinen - O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Clarendon Press, Oxford, 1993. Zbl0780.31001
- [31] E. Ya. Khruslov, The method of orthogonal projections and the Dirichlet problems in domains with a fine-grained boundary, Math. USSR-Sb.17 (1972), 37-59. Zbl0251.35032
- [32] A.A. Kovalevsky, On G-convergence of operators of Dirichlet problem with varying domain, Dokl. Akad. Nauk Ukrain. Ser. A5 (1993), 13-17. Zbl0817.47066
- [33] N. Labani - C. Picard, 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. Zbl0782.35006
- [34] O.A. Ladyzhenskaya - N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002
- [35] J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris, 1969. Zbl0189.40603
- [36] A. Malusa - L. Orsina, Existence and regularity results for relaxed Dirichlet problems with measure data, Ann. Mat. Pura Appl., to appear. Zbl0882.35037
- [37] A.V. Marchenko - E. Ya. Khruslov, Boundary Value Problems in Domains with Fine-Granulated Boundaries (in Russian), Naukova Dumka, Kiev, 1974. Zbl0289.35002
- [38] T. Mekkaoui - C. Picard, Error estimate for the homogenization of a quasilinear Dirichlet problem in a periodically perfored domain, Progress in Partial Differential Equations: the Metz Survey2, 185-193, Pitman Res. Notes in Math. 296, Longman, New York, 1993. Zbl0831.35015
- [39] L. Notarantonio, Asymptotic behaviour of Dirichlet problems on a Riemannian manifold, Ricerche Mat. 41 (1992), 327-367. Zbl0802.58058
- [40] I.V. Skrypnik, Nonlinear Elliptic Boundary Value Problems, Teubner-Verlag, Leipzig, 1986. Zbl0617.35001
- [41] I.V. Skrypnik, 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. Zbl0822.35001
- [42] I.V. Skrypnik, Averaging nonlinear Dirichlet problems in domains with channels, Soviet Math. Dokl. 42 (1991), 853-857. Zbl0757.35027
- [43] I.V. Skrypnik, Asymptotic behaviour of solutions of nonlinear elliptic problems in perforated domains, Mat. Sb. (N.S.)184 (1993), 67-90. Zbl0832.35053
- [44] I.V. Skrypnik, Homogenization of nonlinear Dirichlet problems in perforated domains of general structure, Mat. Sb. (N.S.)187 (1996), 125-157. Zbl0874.35012
- [45] I.V. Skrypnik, New conditions for the homogenization of nonlinear Dirichlet problems in perforated domains, Ukrain. Mat. Zh., to appear. Zbl0887.35015
- [46] L. Tartar, Cours Peccot au Collège de France Paris, 1977, partially written in: Murat F.: H-convergence. Séminaire d'Analyse Fonctionnelle et Numérique, Université d'Alger, 1977-78. English translation: Murat F., Tartar L.: H-convergence. Topics in the Mathematical Modelling of Composite Materials, Birkhäuser, Boston, to appear.
- [47] W.P. Ziemer, Weakly Differentiable Functions, Springer-Verlag, Berlin, 1989. Zbl0692.46022
Citations in EuDML Documents
top- Mamadou Sango, Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a domain with fine-grained boundary
- Carlos Conca, François Murat, Claudia Timofte, A generalized strange term in Signorini’s type problems
- B. Amaziane, S. Antontsev, L. Pankratov, A. Piatnitski, Homogenization of -laplacian in perforated domain
- Carmen Calvo-Jurado, Juan Casado-Díaz, Manuel Luna-Laynez, Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets
- Gianni Dal Maso, François Murat, Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
- Ciro D'Apice, Umberto De Maio, Peter I. Kogut, Suboptimal boundary controls for elliptic equation in critically perforated domain
- Carlos Conca, François Murat, Claudia Timofte, A Generalized Strange Term in Signorini's Type Problems
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