Homogenization of non-uniformly bounded operators: Critical barrier for nonlocal effects

Archive for Rational Mechanics and Analysis

Volumn 164, Issue 1, 2002, Pages 73-101

  Briane, Marc ^a  

^a INSA DE RENNES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036025288     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050200196     Document Type: Article

References (12)

1. M. BELLIEUD, & G. BOUCHITTÉ, Homogenization of elliptic problems in a fiber reinforced structure. Nonlocal effects, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 26 (1998), 407-436.
2. A. BEURLING & J. DENY, Espaces de Dirichlet, Acta Matematica 99 (1958), 203-224.
3. M. BRIANE, Homogenization of a class of non-uniformly elliptic monotonic operators, Nonlinear Analysis, Theory, Methods and Applications 48 (2002), 137-158.
4. G. BUTTAZZO & G. DAL MASO, Γ-limits of integral functionals, J. Analyse Math. 37 (1980), 145-185.
5. L. CARBONE & C. SBORDONE, Some properties of Γ-limits of integral functionals,Annali di Matematica Pura ed Applicata 122 (1979), 1-60.
6. V. N. FENCHENKO & E. YA. KHRUSLOV, Asymptotic of solution of differential equations with strongly oscillating matrix of coefficients which does not satisfy the condition of uniform boundedness, Dokl. AN Ukr. SSR 4 (1981).
7. E. YA. KHRUSLOV, Homogenized models of composite media. In: Composite Media and Homogenization Theory, G. DAL MASO & G. F. DELL' ANTONIO editors, Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser 1991, pp. 159-182.
8. J. L. LIONS, Quelques méthodes de résolution de problèmes aux limites non linéaires, Dunod Gauthiers-Villars, Paris, 1969.
9. U. MOSCO, Composite media and asymptotic Dirichlet forms, J. of Functional Analysis 123 (1994), 368-421.
10. F. MOURAT, H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique, 1977-78, Université d'Alger. English translation: F. MURAT & L. TARTAR, H-convergence, Topics in the Mathematical Modelling of Composite Materials, L. CHERKAEV & R.V. KOHN ed., Progress in Nonlinear Differential Equations and their Applications, Birkhäuser, Boston, 1998, pp. 21-43.
11. F. MOURAT, H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique, 1977-78, Université d'Alger. English translation: F. MURAT & L. TARTAR, H-convergence, Topics in the Mathematical Modelling of Composite Materials, L. CHERKAEV & R.V. KOHN ed., Progress in Nonlinear Differential Equations and their Applications, Birkhäuser, Boston, 1998, pp. 21-43.
12. L. TARTAR, Cours Peccot, Collège de France, (1977), partly written in [10].