On an extension of the method of two-scale convergence and its applications

Sbornik Mathematics

Volumn 191, Issue 7-8, 2000, Pages 973-1014

  Zhikov, V V ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034341523     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2000v191n07ABEH000491     Document Type: Article

References (25)

1. E. De Giorgi and S. Spagnolo, "Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine", Boll. Un. Mat. Ital. (8) 1973, 391-411.
2. N. S. Bakhvalov, "Averaging of partial differential equations with rapidly oscillating coefficients", Dokl. Akad. Nauk SSSR 221 (1975), 516-519; English transl. in Soviet Math. Dokl. 16 (1975).
3. N. S. Bakhvalov and G. P. Panasenko, Homogenization of processes in periodic media. Mathematical problems in the mechanics of composite materials., Nauka, Moscow 1984; English transl., Kluwer, Dordrecht 1989.
4. G. Nguetseng, "A general convergence result for a functional related to the theory of homogenization", SIAM J. Math. Anal. 20 (1989), 608-623.
5. G. Allaire, "Homogenization and two-scale convergence", SIAM J. Math. Anal. 23 (1992), 1482-1518.
6. V. V. Zhikov, "Weighted Sobolev spaces", Mat. Sb. 189:8 (1998), 27-58; English transl. in Sb. Math. 189 (1998).
7. V. V. Zhikov, "Connectedness and homogenization. Examples of fractal conductivity", Mat. Sb. 187:8 (1996), 3-40; English transl. in 56. Math. 187 (1996).
8. V. V. Zhikov, "On a homogenization technique for variational problems", Funktsional. Anal. i Prilozhen. 33:1 (1999), 14-29; English transl. in Functional Anal. Appl. 33 (1999).
9. V. V. Zhikov, S. M. Kozlov, and O. A. Oleǐnik, Homogenization of differential operators, Nauka, Moscow 1993. (Russian)
10. V. V. Zhikov, S. M. Kozlov, and O. A. Olejnik [Oleǐnik], Homogenization of differential operators and integral functionals, Springer-Verlag, Berlin 1994.
11. O. A. Oleǐnik, G. A. Iosif'yan, and A. S. Shamaev, Mathematical problems in the theory of strongly inhomogeneous elastic media, Izdat. Moskov. Gos. Univ., Moscow 1990. (Russian)
12. T. Arbogast, J. Douglas, and U. Hornung, "Derivation of the double porosity model of single phase flow via homogenization theory", SIAM J. Math. Anal. 21 (1990), 823-836.
13. U. Hornung and W. Jäger, "Diffusion, convection, adsorption, and reaction of chemicals in porous media", J. Differential Equations. 92:2 (1991), 199-225.
14. A. Bourgeat, A. Mikelič, and A. Pyatnitski, "Modèle de double porosité aléatoire", C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), 99-104.
15. U. Hornung (ed.), Homogenization and porous media, Springer-Verlag, New York 1997.
16. G. V. Sandrakov, "The homogenization of nonstationary equations with contrasting coefficients", Dokl. Ross. Akad. Nauk 335 (1997), 605-608; English transl. in Dokl. Math. 56 (1997).
17. G. V. Sandrakov, "The homogenization of nonstationary problems in the theory of strongly nonuniform elastic media", Dokl. Ross. Akad. Nauk 358 (1998), 308-311; English transl. in Dokl. Math. 57 (1998).
18. I. Ekeland and R. Temam, Convex analysis and variational problems, North-Holland, Amsterdam 1976.
19. G. Allaire, A. Damlamian, and U. Hornung, "Two-scale convergence on periodic surfaces and applications", Mathematical modelling of flow through porous media, World Scientific, Singapore 1995, pp. 15-25.
20. M. Neuss-Radu, "Some extensions of two-scale convergence", C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 899-904.
21. T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin 1966.
22. E. Ya. Khruslov, "Homogenized models of strongly inhomogeneous media", Proceedings of the International Congress of Mathematicians (Zürich, Switzerland, 1994), Birkhäuser, Basel 1995.
23. E. Ya. Khruslov, "An averaged model of a strongly inhomogeneous medium with memory", Uspekhi Mat. Nauk 45:1 (1990), 197-199; English transl. in Russian Math. Surveys 45 (1990).
24. E. Khruslov, "Homogenized models of composite media", Composite media and homogenization theory, Birkhäuser, Basel 1991, pp. 159-182.
25. G. Bouchitté, G. Buttazzo, and P. Seppecher, "Energies with respect to a measure and applications to low dimensional structures", Calc. Var. Partial Differential Equations 5:1 (1997), 37-54.