Marcellini, Paolo Periodic solutions and homogenization of non linear variational problems. (English) Zbl 0395.49007 Ann. Mat. Pura Appl., IV. Ser. 117, 139-152 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 80 Documents MSC: 49J10 Existence theories for free problems in two or more independent variables 93C10 Nonlinear systems in control theory 35J20 Variational methods for second-order elliptic equations 35B10 Periodic solutions to PDEs Keywords:Periodic Solutions; Homogenization of Non Linear Variational Problems × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Ambrosetti, A.; Sbordone, C., Γ^− convergenza e G-convergenza per problemi non lineari di tipo ellittico, Boll. Un. Mat. Ital., 13-A, 352-362 (1976) · Zbl 0345.49004 [2] I. Babuška,Solution of interface problems by homogenization I, II, III, Techn. Note, Univ. of Maryland (1974-75). [3] I. Babuška,Homogenization and its application. Mathematical and computational problems, Proc. Symp. Numerical Sol. Partial Diff. Eq., III, Maryland (1975), Acad. Press, 1976, pp. 89-116. · Zbl 0346.65064 [4] Bakhvalov, N. S., Averaging of partial differential equations with rapidly oscillating coefficients, Dokl. Akad. Nauk SSSR, 221, 516-519 (1975) · Zbl 0331.35009 [5] Bensoussan, A.; Lions, J. L.; Papanicolaou, G., Sur quelques phénomènes asymptotiques stationnaires, C. R. Acad. Sc. Paris, 281, 89-94 (1975) · Zbl 0309.35007 [6] Bensoussan, A.; Lions, J. L.; Papanicolaou, G., Sur quelques phénomènes asymptotiques d’évolution, C. R. Acad. Sc. Paris, 281, 317-322 (1975) · Zbl 0317.35006 [7] Bensoussan, A.; Lions, J. L.; Papanicolaou, G., Sur de nouveaux problèmes asymptotiques, C. R. Acad. Sc. Paris, 282, 143-147 (1976) · Zbl 0317.35007 [8] Bensoussan, A.; Lions, J. L.; Papanicolaou, G., Homogénéisation, correcteurs et problèmes non-linéaires, C. R. Acad. Sc. Paris, 282, 1277-1282 (1976) · Zbl 0331.35006 [9] Boccardo, L.; Capuzzo Dolcetta, I., G-convergenza e problema di Dirichlet unilaterale, Boll. Un. Mat. Ital., 12, 115-123 (1975) · Zbl 0337.35023 [10] Boccardo, L.; Marcellini, P., Sulla convergenza delle soluzioni di disequazioni variazionali, Ann. Mat. Pura Appl., 110, 137-159 (1976) · Zbl 0333.35030 · doi:10.1007/BF02418003 [11] Caligaris, O., Sulla convergenza delle soluzioni di problemi di evoluzione associati a sottodifferenziali di funzioni conversse, Boll. Un. Mat. Ital., 13-B, 778-806 (1976) · Zbl 0351.47049 [12] Colombini, F.; Spagnolo, S., Sur la convergence de solutions d’équations paraboliques avec des coefficients qui dépendent du temps, C. R. Acad. Sc. Paris, 282, 735-737 (1976) · Zbl 0341.35008 [13] De Giorgi, E.; Spagnolo, S., Sulla convergenza degli integrali dell’energia per operatori ellittici del secondo ordine, Boll. Un. Mat. Ital., 8, 391-411 (1973) · Zbl 0274.35002 [14] Lions, J. L., Asymptotic behaviour of solutions of variational inequalities with highly oscillating coefficients, Lect. Notes in Math., Springer, 503, 30-55 (1976) · Zbl 0354.35031 · doi:10.1007/BFb0088745 [15] J. L. Lions,Sur quelques questions d’analyse, de mécanique et de contrôle optimal, Univ. de Montréal (1976). · Zbl 0339.49003 [16] Marcellini, P., Su una convergenza di funzioni convesse, Boll. Un. Mat. Ital., 8, 137-158 (1973) · Zbl 0282.47014 [17] P. Marcellini — C. Sbordone,Homogenization of non-uniformly elliptic operators, Applicable Anal., to appear. · Zbl 0406.35014 [18] Marcellini, P.; Sbordone, C., Sur quelques questions de G-convergence et d’homogénéisation non linéaire, C. R. Acad. Sc. Paris, 284, 535-537 (1977) · Zbl 0353.49015 [19] F. Murat,Sur l’homogénéisation d’inéquations elliptiques du 2ème ordre, relatives au convexe K(ω_1, ω_2)={ v ∈ H_0^1(Ω)|ω_1⩽v⩽ω_2p. p. dans Ω}, Univ. Paris VI, november 1976. [20] Sanchez Palencia, E., Solutions périodiques par rapport aux variables d’espace et applications, C. R. Acad. Sc. Paris, 271, 1129-1132 (1970) · Zbl 0201.43401 [21] Sanchez Palencia, E., Comportement local et macroscopique d’un type de milieux physiques hétérogènes, Internat. J. Engrg. Sci., 12, 331-351 (1974) · Zbl 0275.76032 · doi:10.1016/0020-7225(74)90062-7 [22] Sbordone, C., Sulla G-convergenza di equazioni ellittiche e paraboliche, Ricerche Mat., 24, 76-136 (1975) · Zbl 0348.35007 [23] Sbordone, C., Su alcune applicazioni di un tipo di convergenza variazionale, Ann. Scuola Norm. Sup. Pisa, 2, 617-638 (1975) · Zbl 0317.49012 [24] Spagnolo, S., Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scuola Norm. Sup. Pisa, 22, 571-597 (1968) · Zbl 0174.42101 [25] S. Spagnolo,Convergence in energy for elliptic operators, Proc. Symp. Numerical Sol. Partial Diff. Eq., III, Maryland (1975), Acad. Press, 1976, pp. 469-498. · Zbl 0347.65034 [26] L. Tartar,Quelques remarques sur l’homogénéisation, Colloque France-Japan, 1976. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.