Homogenization structures and applications I

Zeitschrift für Analysis und ihre Anwendungen

Volumn 22, Issue 1, 2003, Pages 73-107

  Nguetseng, Gabriel ^a  

^a UNIVERSITY OF YAOUNDÉ I   (Cameroon)

Author keywords

Gelfand transformation; Homogenization; Homogenization algebra; Homogenization structure

Indexed keywords

EID: 0037224638     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/zaa/1133     Document Type: Article

References (39)

1. Adams, R.: Sobolev Spaces. New York: Acad. Press 1975.
2. Allaire, G.: Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992), 1482 - 1518.
3. p-data. Assympt. Anal. 17 (1998)3, 165 - 184.
4. Bakhvalov, N. and G. Panashenko: Homogenization: Averaging Processes in Periodic Media (Mathematics and its Applications: BVil 36). Dordrecht: Kluwer Acad. Publ. 1989.
5. Bensoussan, A., Lions, J. L. and G. Papanikolaou: Asymptotic Analysis for Periodic Structures. Amsterdam: North-Holland 1978.
6. Berger, M. and B. Gostiaux: Géométrie différentielle: Variétés, courbes et surfaces. Paris: Presses Univ. de France (PUF) 1987.
7. Bourbaki, N.: Intégration, Chap. 1-4. Paris: Hermann 1966.
8. Bourbaki, N.: Intégration, Chap. 5. Paris: Hermann 1967.
9. Bourbaki, N.: Topologie générale, Chap. V - X. Paris: Hermann 1974.
10. Bourbaki, N.: Topologie générale, Chap. I - IV. Paris: Hermann 1971.
11. Bourbaki, N.: Espaces vectoriels topologiques, Chap. I - II. Paris: Hermann 1965.
12. Bourgeat, A., Mikelic, A. and S. Wright: Stochastic two-scale convergence in the mean and applications. J. Reine Angew. Math. 456 (1994), 19 - 51.
13. Cascado-Diaz, J. and I. Gayte: A general compactness result and its application to the two-scale convergence of almost periodic functions. C.R. Acad. Sci. Paris (Série I) 323 (1996), 329 - 334.
14. Dalmaso, G.: An Introduction to Gamma-Convergence. Boston: Birkhauser 1993.
15. Dautrey, J. and J. L. Lions: Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 2. Paris: Masson 1985.
16. Dieudonne, J.: Eléments d'analyse, Vol. VI/Chap. XXII. Paris: Gauthier-Villars 1975.
17. Edwards, R. D.: Functional Analysis. New York et al.: Holt-Rinehart-Winston 1965.
18. q. Bull. Amer. Math. Soc. 13 (1985), 1 - 21.
19. Guichardet: Analyse harmonique commutative. Paris: Dunod 1968.
20. Jikov, V. V., Kozlov, S. M. and O. A. Oleinik: Homogenization of Differential Operators and Integral Functional. Berlin: Springer-Verlag 1994.
21. Kozlov, S. M.: Averaging random structures. Soviet Math. Dokl. 19 (1978), 950 - 954.
22. Kozlov, S. M.: Averaging differential operators with almost periodic rapidly oscillating coefficients. Math. USSR Sb. 35 (1979), 481 - 498.
23. Kozlov, S. M.: Asymptotic behaviour at infinity of fundamental solutions of equations with almost periodic coefficients. Mosc. Univ. Math. Bull. 35 (1980)4, 10 - 16.
24. Larsen, R.: Banach Algebras. New York: Marcel Dekker 1973.
25. Lions, J. L. and E. Magenes: Problèmes aux limtes non homogènes et applications, Vol. 1. Paris: Dunod 1968.
26. Nečas, J.: Les méthodes directes en théorie des équations elliptiques. Praha: Academia 1967.
27. Nguetseng, G.: Almost periodic homogenization: asymptotic analysis of a second order elliptic equation (Publ. math. LAN 01). Univ. Yde I 2000.
28. Nguetseng, G.: Mean value on locally compact abelian groups (to appear).
29. Nguetseng, G. and R. Nzengwa: Homogenization of an elliptic differential equation of order 2m (submitted).
30. Nguetseng, G.: A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989), 608 - 623.
31. Nguetseng, G.: Homogenization structures and applications II (in preparation).
32. Nguetseng, G. and H. Nnang: Homogenization of nonlinear monotone operators bayond the periodic setting (submitted).
33. Nguetseng, G. and J. L. Woukeng: Deterministic homoganization in time of linear and nonlinear parabolic equations (in preparation).
34. Oleinik, O. and V. Zhikov: On the homogenization of elliptic operators with almost periodic coefficients. Rend. Sem. Mat. Fis. Milano 52 (1982), 149 - 166.
35. Papanicolaou, G. S. and S. R. S. Varadhan: Boundary value problems with rapidly oscillating random coefficients. In: Random Fields (eds.: J. Fritz et al.). Amsterdam: North-Holland 1981, pp. 835 - 873.
36. Sanchez-Palencia, E.: Nonhomogeneous Media and Vibration Theory. Berlin: Springer-Verlag 1980.
37. Tartar, L.: Cours Peccot. Paris: Collège de France 1977.
38. Zhikov, V. V. and E. V. Krivenko: Avering of singularly perturbed elliptic operators (in Russian). Mat. Zametki 33 (1983), 571 - 582; Engl. transl.: Math. Notes 33 (1983), 294 - 300.
39. Zhikov, V. V. and E. V. Krivenko: Avering of singularly perturbed elliptic operators (in Russian). Mat. Zametki 33 (1983), 571 - 582; Engl. transl.: Math. Notes 33 (1983), 294 - 300.