bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Visintin, Augusto:
Scale-Transformations of Maximal Monotone Relations in View of Homogenization
Bollettino dell'Unione Matematica Italiana Serie 9 3 (2010), fasc. n.3, p. 591-601, (English)
pdf, djvu. | MR 2742783

Sunto

On the basis of Fitzpatrick's variational formulation of maximal monotone relations, and of Nguetseng's two-scale approach to homogenization, scale-transformations have recently been introduced and used for the periodic homogenization of quasilinear P.D.E.s. This note illustrates some basic results of this method.
Referenze Bibliografiche
[1] G. ALLAIRE, Homogenization and two-scale convergence. S.I.A.M. J. Math. Anal., 23 (1992), 1482-1518. | fulltext (doi) | MR 1185639 | Zbl 0770.35005
[2] V. BARBU, Nonlinear Differential Equations of Monotone Types in Banach Spaces. Springer, Berlin 2010. | fulltext (doi) | MR 2582280 | Zbl 1197.35002
[3] H. BREZIS, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert. North-Holland, Amsterdam 1973. | MR 348562 | Zbl 0252.47055
[4] H. BREZIS - I. EKELAND, Un principe variationnel associé à certaines équations paraboliques. I. Le cas indépendant du temps, and II. Le cas dépendant du temps. C. R. Acad. Sci. Paris Sér. A-B, 282 (1976), 971-974. | MR 637214 | Zbl 0332.49032
[5] G. DAL MASO, An Introduction to $\Gamma$-Convergence. Birkhäuser, Boston 1993. | fulltext (doi) | MR 1201152 | Zbl 0816.49001
[6] E. DE GIORGI - T. FRANZONI, Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 58 (8) (1975), 842-850. | MR 448194
[7] I. EKELAND - R. TEMAM, Analyse Convexe et Problèmes Variationnelles. Dunod Gauthier-Villars, Paris 1974. | MR 463993
[8] S. FITZPATRICK, Representing monotone operators by convex functions. Workshop/Miniconference on Functional Analysis and Optimization (Canberra, 1988), 59-65; Proc. Centre Math. Anal. Austral. Nat. Univ., 20, Austral. Nat. Univ., Canberra, 1988. | MR 1009594 | Zbl 0669.47029
[9] P. MARCELLINI, Periodic solutions and homogenization of nonlinear variational problems. Ann. Mat. Pura Appl., 117 (1978), 139-152. | fulltext (doi) | MR 515958 | Zbl 0395.49007
[10] J.-E. MARTINEZ-LEGAZ - B. F. SVAITER, Monotone operators representable by l.s.c. convex functions. Set-Valued Anal., 13 (2005), 21-46. | fulltext (doi) | MR 2128696 | Zbl 1083.47036
[11] B. NAYROLES, Deux théorèmes de minimum pour certains systèmes dissipatifs. C. R. Acad. Sci. Paris Sér. A-B, 282 (1976), A1035-A1038. | MR 418609 | Zbl 0345.73037
[12] G. NGUETSENG, A general convergence result for a functional related to the theory of homogenization. S.I.A.M. J. Math. Anal., 20 (1989), 608-623. | fulltext (doi) | MR 990867 | Zbl 0688.35007
[13] R. T. ROCKAFELLAR, Convex Analysis. Princeton University Press, Princeton 1969. | MR 274683
[14] A. VISINTIN, Homogenization of the nonlinear Kelvin-Voigt model of viscoelasticity and of the Prager model of plasticity. Continuum Mech. Thermodyn., 18 (2006), 223-252. | fulltext (doi) | MR 2245987 | Zbl 1160.74331
[15] A. VISINTIN, Homogenization of the nonlinear Maxwell model of visco-elasticity and of the Prandtl-Reuss model of elasto-plasticity. Royal Soc. Edinburgh Proc. A, 138 (2008), 1-39. | fulltext (doi) | MR 2488064
[16] A. VISINTIN, Homogenization of nonlinear visco-elastic composites. J. Math. Pures Appl., 89 (2008), 477-504. | fulltext (doi) | MR 2416672 | Zbl 1166.35004
[17] A. VISINTIN, Extension of the Brezis-Ekeland-Nayroles principle to monotone operators. Adv. Math. Sci. Appl., 18 (2008), 633-650. | MR 2489147 | Zbl 1191.47067
[18] A. VISINTIN, Scale-integration and scale-disintegration in nonlinear homogenization. Calc. Var. Partial Differential Equations, 36 (2009), 565-590. | fulltext (doi) | MR 2558331 | Zbl 1184.35041
[19] A. VISINTIN, Scale-transformations in the homogenization of nonlinear magnetic processes. Archive Rat. Mech. Anal. (in press). | fulltext (doi) | MR 2721590 | Zbl 1233.78043
[20] A. VISINTIN, Homogenization of processes in nonlinear visco-elastic composites. Ann. Scuola Norm. Sup. Pisa (in press). | MR 2905380 | Zbl 1242.35033
[21] A. VISINTIN, A minimization principle for monotone equations. (submitted).
[22] A. VISINTIN, Scale-transformations and homogenization of maximal monotone relations, with applications. (forthcoming). | MR 3086566 | Zbl 1302.35042
[23] A. VISINTIN, Homogenization of a parabolic model of ferromagnetism. (forthcoming). | fulltext (doi) | MR 2737216 | Zbl 1213.35066
[24] E. ZEIDLER, Nonlinear Functional Analysis and its Applications. Vol. II/B: Nonlinear Monotone Operators. Springer, New York 1990. | fulltext (doi) | MR 1033498 | Zbl 0684.47029

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali