\(L^ 2-\)lower semicontinuity of functionals of quadratic type. (English) Zbl 0483.49008


49J45 Methods involving semicontinuity and convergence; relaxation
49K10 Optimality conditions for free problems in two or more independent variables
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[1] Carbone, L.; Sbordone, C., Some properties of Γ-limits of integral functionals, Annali di Matem. Pura Appl., (IV), 122, 1-60 (1979) · Zbl 0474.49016
[2] Coifman, R. R.; Fefferman, C., Weighted norm inequalities for maximal functions and singular integrals, Studia Math., 51, 241-250 (1974) · Zbl 0291.44007
[3] De Giorgi, E.; Franzoni, T., Su un tipo di convergenza variazionale, 842-850 (1975), Roma: Rend. Acc. Naz. Lincei, Roma
[4] De Giorgi, E.; Spagnolo, S., Sulla convergenza degli integrali dell’energia per operatori ellittici del 2∘ ordine, Boll. U.M.I., 8, 391-411 (1973) · Zbl 0274.35002
[5] I.Ekeland - R.Temam,Analyse convexe et problèmes variationnels, Dunod-Gauthier-Villars, 1974. · Zbl 0281.49001
[6] I.Gilbarg - N.Trudinger,Elliptic partial differential equations of second order, Springer Verlag, (1977). · Zbl 0361.35003
[7] F.Liu,A Luzin type property of Sobolev functions, Indiana University Math. Journal,26, no. 4 (1977). · Zbl 0368.46036
[8] P.Marcellini,Some problems of semicontinuity and of Γ-convergence for integrals of the Calculus of Variations, Proc. of the Int. Coll. «Metodi recenti di Analisi non lineare e Applicazioni», Roma, May 1978.
[9] Marcellini, P.; Sbordone, C., Homogeneization of non-uniformly elliptic operators, Applicable Analysis, 8, 101-113 (1978) · Zbl 0406.35014
[10] Meyers, N. G.; Serrin, J., H=W, Proc. Nat. Acad. Sci. U.S.A., 51, 1055-1056 (1964) · Zbl 0123.30501
[11] C. B.Morrey,Multiple integrals in the Calculus of Variations, Springer, 1966. · Zbl 0142.38701
[12] F.Murat,H-Convergence, Séminaire d’Analyse Fonctionnelle et Numerique 77-78 de l’Université d’Alger.
[13] Trudinger, N., Linear elliptic operators with measurable coefficients, Ann. Scuola Norm. Sup. Pisa, 27, 265-308 (1973) · Zbl 0279.35025
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