References
L. Ambrosio,Nuovi risultati sulla semicontinuità inferiore di certi funzionali integrali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.,79, (5), pp. 82–89.
L. Ambrosio,New lower semicontinuity results for integral functionals, Rend. Accad. Naz. Sci. XL Mem. Mat. Fis. Natur.,105 (1987), pp. 1–42
L. Ambrosio—O. Ascenzi—G. Buttazzo,Lipschitz regularity for minimizers of integral functionals with high discontinuous integrands, Preprint University of Pisa, to appear on the Journal of Mathematical Analysis and Applications.
L. Ambrosio—G. Buttazzo—A. Leaci,Continuous operators of the form T f (u)=f(x, u, Du), submitted to Boll. Un. Mat. Ital.
G. Buttazzo—G. Dal Maso,A characterization of nonlinear functionals on Sobolev spaces which admit an integral representation with a Caratheodory integrand, J. Math. Pures Appl.,64 (1985), pp. 337–361.
G. Buttazzo—G. Dal Maso,Λ-limits of integral functionals, J. Analyse Math.,37 (1980), pp. 145–185.
G. Buttazzo—A. Leaci,A continuity theorem for operators from W 1, q (Ω) into L r (Ω), J. Funct. Anal.,58 (1984), pp. 216–224.
G. Buttazzo—A. Leaci,Relaxation results for a class of variational integrals, J. Funct. Anal.,61 (1985), pp. 360–377.
C. Castaing—M. Valadier,Convex analysis and measurable multifunctions, Lecture Notes in Mathematics.,580, Springer-Verlag, Berlin (1977).
L. Cesari,Optimization. Theory and Applications, Springer-Verlag, Berlin (1983).
I. Ekeland—R. Teman,Convex Analysis and Variational Problems, North-Holland, Amsterdam (1978).
D. Gilbarg—N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin (1983).
E. De Giorgi—G. Buttazzo—G. Dal Maso,On the lower semicontinuity of certain integral functionals, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.,74 (1983), pp. 274–282.
F.C. Liu,A Luzin type property of Sobolev functions, Indiana Univ. Math. J.,26 (1977).
P. Marcellini—C. Sbordone,Semicontinuity problems in the calculus of variations, Nonlinear Anal.,4 (1980), pp. 241–257.
M. Marcus—V. J. Mizel,Absolute continuity of tracks and mappings of Sobolev spaces, Arch. Rational. Mech. Anal.,45 (1972), pp. 294–320.
J. Serrin,On the definition and properties of certain variational integrals, Trans. Amer. Mat. Soc.,101 (1961), pp. 139–167.
J. Serrin—D. E. Varberg,A general chain rule for derivatives and the change of variables formula for the Lebesque integral, Amer. Math. Monthly,76 (1969), pp. 514–520.
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Ambrosio, L. Relaxation of autonomous functionals with discontinuous integrands. Ann. Univ. Ferrara 34, 21–47 (1988). https://doi.org/10.1007/BF02824972
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DOI: https://doi.org/10.1007/BF02824972