Homogenization of almost periodic monotone operators

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1. [1] N.S. Bakhvalov and G.P. Panasenko, Averaged Processes in Periodic Media, Nauka, Moscow, 1984. Zbl0607.73009MR797571
2. [2] A. Bensoussan, J.L. Lions and G.C. Papanicolaou, Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam, 1978. Zbl0404.35001MR503330
3. [3] A. Besicovitch, Almost Periodic Functions, Cambridge, 1932. Zbl0004.25303JFM58.0264.02
4. [4] L. Boccardo and Th. Gallouet, Homogenization with Jumping Nonlinearities, Ann. Mat. Pura Appl., (4), Vol. 138, 1984, pp. 211-221. Zbl0568.35038MR779543
5. [5] L. Boccardo and F. Murat, Homogénéisation de problèmes quasi linéaires, Studio di problemi-limite della Analisi Funzionale (Bressanone, 1081), 13-51, Pitagora Editrice, Bologna, 1982. 
6. [6] L. Boccardo and F. Murat, Remarques sur l'homogénéisation de certains problèmes quasi-linéaires, Portugal. Math., Vol. 41, 1982, pp. 535-562. Zbl0524.35042MR766874
7. [7] A. Braides, Omogeneizzazione di integrali non coercivi, Ricerche Math., Vol. 32, 1983, pp. 347-368. Zbl0547.49007
8. [8] A. Braides, Homogenization of Some Almost Periodic Coercive Functionals, Rend. Accad. Naz. XL, Vol.9, 1985, pp. 313-322. Zbl0582.49014MR899255
9. [9] A. Braides, A Homogenization Theorem for Weakly Almost Periodic Functionals, Rend. Accad. Naz. XL, Vol. 10, 1986, pp. 261-281. Zbl0611.49007MR879115
10. [10] A. Braides, Correctors for the Homogenization of Almost Periodic Monotone Operators, Asympt. Anal., Vol. 5, 1991, pp. 47-74. Zbl0768.35005MR1132080
11. [11] A. Braides , Almost Periodic Methods in the Theory of Homogenization, Applicable Anal. (to appear). MR1307012
12. [12] E. Cabib and C. Davini, On the Variational Convergence with a Null Divergence Condition, Preprint, Università di Udine, 1989. Zbl0729.49005MR1110674
13. [13] E. Cabib, C. Davini and C.Q. Ru, A Problem in the Optimal Design of Networks Under Transverse Loading, Quart. Appl. Math., Vol. 48, 1990, pp. 251-263. Zbl0706.73057MR1052135
14. [14] S. Campanato, Sistemi ellittici in forma divergenza. Regolarità all'interno. Quaderni Scuola Normale Sup., Pisa, 1980. Zbl0453.35026MR668196
15. [15] L. Carbone and C. Sbordone, Some Properties of Γ-Limits of Integral Functionals, Ann. Mat. Pura Appl., (4), Vol. 122, 1979, pp. 1-60. Zbl0474.49016MR565062
16. [16] V. Chiadó Piat, G. Dal Maso and A. Defranceschi, G-Convergence of Monotone Operators, Ann. Inst. H. Poincaré. Anal. Non Linéaire, Vol. 7, 1990, pp. 123-160. Zbl0731.35033MR1065871
17. [17] V. Chiadò Piat and A. Defranceschi, Homogenization of Monotone Operators, Nonlinear Anal., Vol. 14, 1990, pp. 717-732. Zbl0705.35041MR1049117
18. [18] G. Dal Maso and A. Defranceschi, Correctors for the Homogenization of Monotone Operators, Diff. Integral Eq., Vol. 3, 1990, pp. 1151-1166. Zbl0733.35005MR1073064
19. [19] G. Dal Maso and L. Modica, Integral Functionals Determined by their Minima, Rend. Sem. Mat. Univ. Padova, Vol. 76, 1986, pp. 255-267. Zbl0613.49028MR881574
20. [20] R. De Arcangelis, A General Homogenization Result for Almost Periodic Functionals, J. Math. Anal. Appl., Vol. 156, (2), 1991, pp. 358-380. Zbl0743.49019MR1103018
21. [21] E. De Giorgi and S. Spagnolo, Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine, Boll. Un. Mat. Ital., (4), Vol. 8, 1973, pp. 391- 411. Zbl0274.35002MR348255
22. [22] T. Del Vecchio, On the Homogenization of a Class of Pseudomonotone Operators in Divergence Form, Boll. Un. Mat. Ital., Vol. 5-B, 1991, pp. 369-388. Zbl0777.47026MR1111128
23. [23] J. Francù, Homogenization and Correctors for Nonlinear Elliptic Equations, Comment. Math. Univ. Carolin. (to appear). Zbl0728.35007
24. [24] N. Fusco and G. Moscariello, L2-Lower Semicontinuity of Functionals of Quadratic Type, Ann. Mat. Pura Appl., (4), Vol. 129, 1981, pp. 306-326. Zbl0483.49008MR648337
25. [25] N. Fusco and G. Moscariello, Further Results on the Homogenization of Quasilinear Operators, Ricerche Mat., Vol. 35, 1986, pp.231-246. Zbl0658.35016MR932435
26. [26] N. Fusco and G. Moscariello, On the Homogenization of Quasilinear Divergence Structure Operators, Ann. Mat. Pura Appl., Vol. 146, 1987, pp. 1-13. Zbl0636.35027MR916685
27. [27] D. Kinderlehrer and S. Stampacchia, An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. Zbl0457.35001MR567696
28. [28] S.M. Kozlov, Averaging Differential Operators with Almost-Periodic Rapidly Oscillating Coefficients, Math. USSR-Sb., Vol. 35, 1979, pp.481-498. Zbl0422.35003MR512007
29. [29] S.M. Kozlov, Reducibility of Quasiperiodic Differential Operators and Averaging, Trans. Moscow Math. Soc., Vol. 2, 1984, pp. 101-126. Zbl0566.35036
30. [30] B.M. Levitan and V.V. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge Univ. Press, Cambridge, 1982. Zbl0499.43005MR690064
31. [31] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
32. [32] P. Marcellini, Periodic Solutions and Homogenization of Non Linear Variational Problems, Ann. Mat. Pura Appl., (4), Vol. 117, 1978, pp. 139-152. Zbl0395.49007MR515958
33. [33] N.G. Meyers and A. Elcrat, Of Non-Linear Elliptic Systems and Quasi-Regular Functions, Duke Math. J., Vol. 42, 1975, pp. 121-136. Zbl0347.35039MR417568
34. [34] F. Murat, H-convergence, Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger, 1977. 
35. [35] F. Murat, Compacité par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4), Vol. 5, 1978, pp. 489-507. Zbl0399.46022MR506997
36. [36] O.A. Oleinik and V.V. Zhikov, On the Homogenization of Elliptic Operators with Almost-Periodic Coefficients, Rend. Sem. Mat. Fis. Milano, Vol. 52, 1982, pp. 149-166. Zbl0568.35029MR802999
37. [37] U.E. Raitum, On the G-Convergence of Quasilinear Elliptic Operators with Unbounded Coefficients, Soviet Math. Dokl., Vol. 24, 1981, pp. 472-476. Zbl0501.35033MR636853
38. [38] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966. Zbl0142.01701MR210528
39. [39] E. Sanchez-Palencia, Non Homogeneous Media and Vibration Theory, Lect. Notes Phys., 127, Springer-Verlag, Berlin, 1980. Zbl0432.70002
40. [40] S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore, Ann. Scuola Norm. Sup. Pisa Cl. Sci., (3), Vol. 21, 1967, pp. 657-699. Zbl0153.42103MR225015
41. [41] S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scuola Norm. Sup. Pisa Cl. Sci., (3), Vol. 22, 1968, pp. 577-597. Zbl0174.42101MR240443
42. [42] S. Spagnolo, Convergence in Energy for Elliptic Operators, Proc. Third Symp. Numer. Solut. Partial Diff. Equat., College Park, 1975, pp.469-498, Academic Press, New York, 1976. Zbl0347.65034MR477444
43. [43] L. Tartar, Cours Peccot, Collège de France, Paris, 1977. 
44. [44] L. Tartar, Quelques remarques sur l'homogénéisation, Proc. of the Japan-France seminar 1976 "Functional analysis and numerical analysis", pp. 469-482, Japan Society for the Promotion of Science, 1978. 
45. [45] L. Tartar, Compensated Compactness and Partial Differential Equations, Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. IV, pp. 136-212, Pitman, London, 1979. Zbl0437.35004MR584398
46. [46] L. Tartar, Homogénéisation d'opérateurs monotones, Manuscript, 1981. 
47. [47] V.V. Zhikov, S.M. Kozlov, O.A. Oleinik and Kha T'en Ngoan, Averaging and G-Convergence of Differential Operators, Russian Math. Surveys, Vol. 34, 1979, pp. 69-147. Zbl0445.35096MR562800

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