Homogenization of Neumann problems for unbounded integral functionals

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1. ANNIN, B. D., Existence and uniqueness of the solution of the elastic-plastic torsion problem for a cylindrical bar of oval cross-section, J. Appl. Math. Mech., 29 (1965), 1038-1047. Zbl0158.21604
2. ATTOUCH, H., Introduction a l'homogenisation d'inequations variationnelles, Rend. Sem. Mat. Univ. Politecn. Torino, 40 (1982), 1-23. Zbl0523.35004MR724197
3. ATTOUCH, H., Variational Convergence for Functions and Operators, Pitman (1984). Zbl0561.49012MR773850
4. BENSOUSSAN, A.- LIONS, J. L.- PAPANICOLAOU, G., Asymptotic Analysis for Periodic Structures, Stud. Math. Appl., 5, North Holland (1978). Zbl0404.35001MR503330
5. BREZIS, H., Multiplicateur de Lagrange en torsion elasto-plastique, Arch. Rational Mech. Anal., 49 (1973), 32-40. Zbl0265.35021MR346346
6. BREZIS, H.- SIBONY, M., Équivalence de deux inéquations variationnelles et applications, Arch. Rational Mech. Anal., 41 (1971), 254-265. Zbl0214.11104MR346345
7. BUTTAZZO, G., Su una definizione generale dei $\mathrm{\Gamma }$-limiti, Boll. Un. Mat. Ital. (5), 14-B (1977), 722-744. Zbl0445.49016MR500789
8. CAFFARELLI, A.- RIVIERE, N. M., On the Lipschitz character of the stress tensor when twisting an elastic-plastic bar, Arch. Rational Mech. Anal., 69 (1979), 31-36. Zbl0399.73044MR513957
9. CARBONE, L., Sur la convergence des intégrales du type de l'énergie sur des fonctions a gradient borné, J. Math. Pures Appl., 56 (1977), 79-84. Zbl0308.49023MR482459
10. CARBONE, L., $\mathrm{\Gamma }$-convergence d'intégrales sur des functions avec des contraintes sur le gradient, Comm. Partial Differential Equations, 2 (1977), 627-651. Zbl0357.49020MR493642
11. CARBONE, L., Sull'omogeneizzazione di un problema variazionale con vincoli sul gradiente, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (8), Mat. Appl., 63 (1977), 10-14. Zbl0395.49029
12. CARBONE, L., Sur un problème d'homogénéisation avec des contraintes sur le gradient, J. Math. Pures Appl., 58 (1979), 275-297. Zbl0387.49028MR544254
13. CARBONE, L.- DE ARCANGELIS, R., On integral representation, relaxation and homogenization for unbounded functionals, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9), Mat. Appl., 8 (1997), 129-135. Zbl0891.49006MR1485325
14. CARBONE, L.- DE ARCANGELIS, R., Unbounded functionals: applications to the homogenization of gradient constrained problems, to appear on Ricerche Mat.. Zbl0962.49011MR1757294
15. CARBONE, L.- SALERNO, S., On a problem of homogenization with quickly oscillating constraints on the gradient, J. Math. Anal. Appl., 90 (1982), 219-250. Zbl0499.49007MR680876
16. CARBONE, L.- SALERNO, S., Further results on a problem of homogenization with constraints on the gradient, J. Analyse Math., 44 (1984/85), 1-20. Zbl0574.35006MR801284
17. CARBONE, L.- SALERNO, S., Homogenization with unbounded constraints on the gradient, Nonlinear Anal., 9 (1985), 431-444. Zbl0557.49006MR785715
18. CARBONE, L.- SBORDONE, C., Some properties of $\mathrm{\Gamma }$-limits of integral functionals, Ann. Mat. Pura Appl. (4), 122 (1979), 1-60. Zbl0474.49016MR565062
19. CIORANESCU, D.- SAINT JEAN PAULIN, J., Homogenization in open sets with holes, J. Math. Anal. Appl., 71 (1979), 590-607. Zbl0427.35073MR548785
20. CORBO ESPOSITO, A.- DE ARCANGELIS, R., The Lavrentieff phenomenon and different processes of homogenization, Comm. Partial Differential Equations, 17 (1992), 1503-1538. Zbl0814.35006MR1187620
21. CORBO ESPOSITO, A.- DE ARCANGELIS, R., Homogenization of Dirichlet problems with nonnegative bounded constraints on the gradient, J. Analyse Math., 64 (1994), 53-96. Zbl0822.49012MR1303508
22. CORBO ESPOSITO, A.- DE ARCANGELIS, R., Some notes on a characterization of function sets described by constraints on the gradient, in Nonlinear Variational Problems and Partial Differential Equations, A. Marino and M.K.V. Murthy editors, Pitman Res. Notes Math. Series, 320, Longman Scientific & Technical (1995), 182-196. Zbl0833.46021
23. CORBO ESPOSITO, A.- SERRA CASSANO, F., A Lavrentieff phenomenon for problems of homogenization with constraints on the gradient, Ricerche Mat., 46 (1997), 127-159. Zbl0946.49009MR1615766
24. DAL MASO, G., An Introduction to $\mathrm{\Gamma }$-Convergence, Progr. Nonlinear Differential Equations Appl., 8, Birkhäuser (1993). Zbl0816.49001MR1201152
25. DE ARCANGELIS, R.- GARGIULO, G., Homogenization of integral functionals with linear growth defined on vector-valued functions, NoDEA Nonlinear Differential Equations Appl., 2 (1995), 371-416. Zbl0839.49012MR1343400
26. DE ARCANGELIS, R.- GAUDIELLO, A.- PADERNI, G., Some cases of homogenization of linearly coercive gradient constrained variational problems, Math. Models Methods Appl. Sci., 6 (1996), 901-940. Zbl0876.49012MR1419237
27. DE ARCANGELIS, R.- VITOLO, A., Some cases of homogenization with unbounded oscillating constraints on the gradient, Asymptotic Anal., 5 (1992), 397-428. Zbl0769.49029MR1159380
28. DE GIORGI, E., $G$-operators and $\mathrm{\Gamma }$-convergence; in Proceedings of the International Congress of Mathematicians, Warszawa, August 16-24, 1983, PWN, Warszawa (1984), 1175-1191. Zbl0568.35025
29. DE GIORGI, E.- FRANZONI, T., Su un tipo di convergenza variazionale, Rend. Sem. Mat. Brescia, 3 (1979), 63-101. Zbl0339.49005
30. DE GIORGI, E.- SPAGNOLO, S., Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine, Boll. Un. Mat. Ital. (4), 8 (1973), 391-411. Zbl0274.35002MR348255
31. DE MAIO, U.- DURANTE, T., Homogenization of Dirichlet problems for some types of integral functionals, to appear on Ricerche Mat. Zbl0945.49006MR1615758
32. DUVAUT, G.- LANCHON, H., Sur la solution du problème de torsion élastoplastique d'une barre cylindrique de section quelconque, C. R. Acad. Sci. Paris Sér. I Math., 264 (1967), 520-523. Zbl0152.43404MR232569
33. DUVAUT, G.- LIONS, J.L., Inequalities in Mechanics and Physics, Springer-Verlag (1976). Zbl0331.35002MR521262
34. FUSCO, N., $\mathrm{\Gamma }$-convergenza unidimensionale, Boll. Un. Mat. Ital. (5), 16-B (1979), 74-86. Zbl0403.49015MR536528
35. GLOWINSKI, R.- LANCHON, H., Torsion élastoplastique d'une barre cylindrique de section multiconnexe, J. Mécanique, 12 (1973), 151-171. Zbl0273.73023MR363114
36. LANCHON, H., Torsion élastoplastique d'une barre cylindrique de section simplement ou multiplement connexe, J. Mécanique, 13 (1974), 267-320. Zbl0285.73020MR363107
37. MARCELLINI, P., Periodic solutions and homogenization of non linear variational problems, Ann. Mat. Pura Appl. (4), 117 (1978), 139-152. Zbl0395.49007MR515958
38. MARCELLINI, P.- SBORDONE, C., Homogenization of non-uniformly elliptic operators, Appl. Analysis, 8 (1978), 101-113. Zbl0406.35014MR523948
39. MURAT, F.- TARTAR, L., $H$-convergence, in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev and R. Kohn editors, Progr. Nonlinear Differential Equations Appl., 31, Birkäuser (1997), 21-44. Zbl0920.35019MR1493039
40. SANCHEZ.PALENCIA, E., Nonhomogeneous Media and Vibration Theory, Lecture Notes in Phys., 127, Springer-Verlag (1980). Zbl0432.70002MR578345
41. TING, T. W., Elastic-plastic torsion of simply connected cylindrical bars, Indiana Univ. Math. J., 20 (1971), 1047-1076. Zbl0205.56203MR277161
42. ZHIKOV, V. V.- KOZLOV, S. M.- OLEINIK, O. A.- T'EN NGOAN, Averaging and $G$-convergence of differential operators, Russian Math. Surveys, 34 (1979), 69-147. Zbl0445.35096MR562800

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