Homogenization of a monotone problem in a domain with oscillating boundary

Mathematical Modelling and Numerical Analysis

Volumn 33, Issue 5, 1999, Pages 1057-1070

  Blanchard, Dominique ^a   Carbone, Luciano ^b   Gaudiello, Antonio ^b  

^a UNIVERSITÉ DE ROUEN   (France)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033422810     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:1999134     Document Type: Article

References (25)

1. E. Acerbi and D. Percivale, Homogenization of Noncoercive Functionals: Periodic Materials with Soft Inclusions. Appl. Math. Optim. 17 (1988) 91-102.
2. H. Attouch, Variational Convergence for Functions and Operators. Applicable Mathematics Series, Pitman, London (1984).
3. N. Bakhvalov and G. Panasenko, Homogenization: Averaging Processes in Periodic Media, in Mathematics and Its Applications, Vol. 36, Kluwer Academic Publishers (1989).
4. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures. North Holland, Amsterdam (1978).
5. R. Brizzi and J.P. Chalot, Homogénéisation de frontière. Doctoral Dissertation, University of Nice (1978).
6. R. Brizzi and J.P. Chalot, Boundary Homogenization and Neumann Boundary Value Problem. Ric. Mat. 46 (1997) 341-387.
7. G. Buttazzo and R.V. Kohn, Reinforcement by a Thin Layer with Oscillating Thickness. Appl. Math. Optim. 16 (1987) 247-261.
8. A. Corbo Esposito, P. Donato, A. Gaudiello and C. Picard, Homogenization of the p-Laplacian in a Domain with Oscillating Boundary. Comm. Appl. Nonlinear Anal. 4 (1997) 1-23.
9. V. Chiadò Piat, Convergence of Minima for non Equicoercive Functionals and Related Problems. Ann. Mat. Pura Appl. 157 (1990) 251-283.
10. V. Chiadò Piat, G. Dal Masso and A. Defranceschi, G-Convergence of Monotone Operators. Ann. Inst. H. Poincaré 7 (1990) 123-160.
11. G. Dal Masso, An Introduction to Γ-Convergence. Birkhäuser Boston (1993).
12. E. De Giorgio and T. Franzoni, Su un tipo di convergenza variazionale. Rend. Sem. Mat. Brescia 3 (1979) 63-101.
13. e Cycle, University of Nice, France (1974).
14. P. Donato and G. Moscariello, On the Homogenization of Some Nonlinear Problems in Perforated Domains. Rend. Sem. Mat. Univ. Padova 84 (1990) 91-108.
15. N. Fusco and G. Moscariello, On the Homogenization of Quasilinear Divergence Structure Operators. Ann. Mat. Pura Appl. 146 (1987) 1-13.
16. A. Gaudiello, Asymptotic Behaviour of non-Homogeneous Neumann Problems in Domains with Oscillating Boundary. Ric. Mat. 43 (1994) 239-292.
17. J.L. Lions, Quelques méthodes de résolution de problèmes aux limites non linéaires. Dunod, Paris (1969).
18. J.L. Lions, Some Aspects of Optimal Control of Distributed Parameter Systems. SIAM Monograph 6 (1972).
19. F. Murat and A. Sili, Problèmes monotones dans des cylindres de faible diamètre. C.R. Acad. Sci. Paris Sér. I 319 (1994) 567-572.
20. F. Murat and A. Sili, Problèmes monotones dans des cylindres de faible diamètre formés de matériaux hétérogènes. C.R. Acad. Sci. Paris Sér. I 320 (1995) 1199-1204.
21. F. Murat and J. Simon, Quelques résultats sur le contrôle par un domaine géométrique. Report 74003, Lab. Num. Analysis, University of Paris VI, France (1974).
22. O. Pironneau, Sur les problèmes d'optimisation de structure en mécanique des fluides. Thèse d'État, University of Paris VI, France (1976).
23. O. Pironneau and C. Saguez, Asymptotic Behavior, with respect to the Domain, of Solutions of Partial Differential Equations. IRIA-LABORIA, Report 212 (1977).
24. E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory. Lect. Notes Phys. 127, Springer, Berlin (1980).
25. L. Tartar, Cours Peccot, Collège de France (1977). Partially written in F. Murat, H-Convergence, Séminaire d'analyse fonctionnelle et numérique de l'Université d'Alger (1977-78). English translation in Mathematical Modelling of Composite Materials, A. Cherkaev and R.V. Kohn Ed., Progress in Nonlinear Differential Equations and their Applications, Birkhäuser-Verlag (1997) 21-44.