Free access
Issue
ESAIM: M2AN
Volume 37, Number 5, September-October 2003
Page(s) 773 - 805
DOI http://dx.doi.org/10.1051/m2an:2003055
Published online 15 November 2003
  1. N. Ansini and A. Braides, Asymptotic analysis of periodically perforated non-linear media. J. Math. Pures Appl. 81 (2002) 439-451. [CrossRef] [MathSciNet]
  2. H. Attouch, Variational Convergence for Functions and Operators. Pitman, London (1984).
  3. A. Braides and A. Defranceschi, Homogenization of Multiple Integrals. Oxford University Press, Oxford (1998).
  4. H. Brézis, Problèmes unilatéraux. J. Math. Pures Appl. 51 (1972) 1-168. [MathSciNet]
  5. C. Calvo Jurado and J. Casado Díaz, The limit of Dirichlet systems for variable monotone operators in general perforated domains. J. Math. Pures Appl. 81 (2002) 471-493. [CrossRef] [MathSciNet]
  6. J. Casado Díaz, Existence of a sequence satisfying Cioranescu-Murat conditions in homogenization of Dirichlet problems in perforated domains. Rend. Mat. Appl. 16 (1996) 387-413. [MathSciNet]
  7. J. Casado-Díaz, Homogenization of Dirichlet problems for monotone operators in varying domains. Proc. Roy. Soc. Edinburgh Sect. A 127 (1997) 457-478. [MathSciNet]
  8. D. Cioranescu and J. Saint Jean Paulin, Homogenization in open sets with holes. J. Math. Anal. Appl. 71 (1979) 590-607. [CrossRef] [MathSciNet]
  9. D. Cioranescu and F. Murat, Un terme étrange venu d'ailleurs, I and II, in Nonlinear Differential Equations and Their Applications, Collège de France Seminar, H. Brézis and J.L. Lions, Eds., Vol. II, pp. 98-138, Vol. III, pp. 154-178. Pitman, London, Research Notes in Mathematics 60 and 70 (1982 and 1983). English translation: A Strange Term Coming from Nowhere, in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev and R.V. Kohn, Eds. Birkhäuser, Boston, Progr. Nonlinear Differential Equations Appl. 31 (1997) 45-93.
  10. C. Conca and P. Donato, Non homogeneous Neumann problems in domains with small holes. RAIRO Modél. Math. Anal. Numér. 22 (1988) 561-607. [MathSciNet]
  11. C. Conca and M. Vanninathan, On uniform H2-estimates in periodic homogenization. Proc. Roy. Soc. Edinburgh A 131 (2001) 499-517. [CrossRef] [MathSciNet]
  12. G. Dal Maso, On the integral representation of certain local functionals. Ricerche Mat. 32 (1983) 85-113. [MathSciNet]
  13. G. Dal Maso, Γ-convergence and µ-capacities. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 14 (1987) 423-464. [MathSciNet]
  14. G. Dal Maso, An Introduction to Γ-Convergence. Birkhäuser, Boston, Progr. Nonlinear Differential Equations Appl. 8 (1993).
  15. G. Dal Maso and A. Garroni, New results on the asymptotic behavior of Dirichlet problems in perforated domains. Math. Models Methods Appl. Sci. 4 (1994) 373-407. [CrossRef] [MathSciNet]
  16. G. Dal Maso and F. Murat, Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. Ann. Scuola. Norm. Sup. Pisa Cl. Sci. 24 (1997) 239-290. [MathSciNet]
  17. G. Dal Maso and F. Murat, Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains. Ann. Inst. H. Poincaré, Anal. non linéaire (to appear).
  18. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale. Atti. Accad. Naz. Lincei Rend. Cl. Sci. Mat. Fis. Natur. 58 (1975) 842-850.
  19. G. Duvaut and J.L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972).
  20. G. Fichera, Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno. Mem. Accad. Naz. Lincei, Serie 8 7 (1964) 91-140.
  21. A. Kovalevsky, An effect of double homogenization for Dirichlet problems in variable domains of general structure. C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 1151-1156.
  22. J.L. Lions and G. Stampacchia, Variational inequalities. Comm. Pure Appl. Math. 20 (1967) 493-519. [CrossRef] [MathSciNet]
  23. V.A. Marcenko and E.Ja. Hrouslov, Boundary Value Problems in Domains with Fine-Grained Boundary (in russian). Naukova Dumka, Kiev (1974).
  24. F. Murat, H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique de l'université d'Alger 1977-1978, multigraphied, 34 p. English translation: F. Murat and L. Tartar, H-convergence, in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev and R.V. Khon, Eds. Birkhäuser, Boston, Progr. Nonlinear Differential Equations Appl. 31 (1997) 21-43.
  25. A. Signorini, Sopra alcune questioni di Elastostatica. Atti della Soc. Ital. per il Progresso della Scienze (1963).
  26. I.V. Skrypnik, Nonlinear Elliptic Boundary Value Problems. Teubner-Verlag, Leipzig (1986).
  27. L. Tartar, Problèmes d'homogénéisation dans les équations aux dérivées partielles. Cours Peccot, Collège de France (1977) (Partially written in []).
  28. L. Tartar, Quelques remarques sur l'homogénéisation, in Functional Analysis and Numerical Analysis, Proceedings of the Japan-France Seminar 1976, H. Fujita, Ed. Japan Society for the Promotion of Science, Tokyo (1978) 469-482.

Recommended for you