On the lower semicontinuity of supremal functionals defined on measures
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 327-369.

Voir la notice de l'article dans Biblioteca Digitale Italiana di Matematica

In questo lavoro si considerano due particolari classi di funzionali supremali definiti sulle misure di Radon e si determinano alcune condizioni necessarie e sufficienti alla loro semicontinuità rispetto alla convergenza debole*. Vengono successivamente presentate alcune applicazioni di questi risultati alla minimizzazione di opportuni funzionali definiti su BV. 
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Gori, Michele. On the lower semicontinuity of supremal functionals defined on measures. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 327-369. https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a6/

[1] E. Acerbi - G. Buttazzo - N. Prinari, The class of functionals which can be represented by a supremum, J. Convex Analysis, 9 (2002), 225-236. | Zbl

[2] R. Alicandro - A. Braides - M. Cicalese, $L^\infty$ energies on discontinuous functions, Preprint.

[3] L. Ambrosio, Existence theory for a new class of variational problems, Arch. Rational Mech. Anal., 111 (1990), 291-322. | Zbl

[4] L. Ambrosio - G. Buttazzo, Weak lower semicontinuous envelope of functions defined on a space of measures, Ann. Mat. pura appl., 150 (1988), 311-340. | Zbl

[5] L. Ambrosio - G. Dal Maso, On the relaxation in $BV(\Omega, \mathbb{R}^m)$ of quasi-convex integrals, J. Func. Anal., 109 (1992), 76-97. | Zbl

[6] L. Ambrosio - N. Fusco - D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford University Press, Inc. New York, 2000. | Zbl

[7] G. Anzellotti - G. Buttazzo - G. Dal Maso, Dirichlet problem for demi-coercive functionals, Nonlinear Anal., 10 (1986), 603-613. | Zbl

[8] G. Aronsson - M.G. Crandall - P. Juutinen, A tour of the theory of absolutely minimizing functions, Bull. Amer. Math. Soc. (N.S.), 41 (2004),no. 4, 439-505. | Zbl

[9] E.N. Barron - R.R. Jensen - C.Y. Wang, Lower semicontinuity of $L^\infty$ functionals, Ann. I. H. Poincaré - AN 18 (2001), 495-517. | fulltext EuDML | Zbl

[10] E.N. Barron - W. Liu, Calculus of variations in $L^\infty$, Appl. Math. Optim., 35 (1997), 237-263. | Zbl

[11] G. Bouchitté, Représentation intégrale de fonctionelles convexes sur un espace de measures, Ann. Univ. Ferrara, 18 (1987), 113-156. | Zbl

[12] G. Bouchitté - G. Buttazzo, New lower semicontinuity results for nonconvex functionals defined on measures, Nonlinear Anal., 15 (1990), 679-692. | Zbl

[13] G. Bouchitté - G. Buttazzo, Integral representation of nonconvex functionals defined on measures, Ann. Inst. Henri Poincaré, 9 (1992), 101-117. | fulltext EuDML | Zbl

[14] G. Bouchitté - G. Buttazzo, Relaxation for a class of nonconvex functionals defined on measures, Ann. Inst. Henri Poincaré, 10 (1993), 345-361. | fulltext EuDML | Zbl

[15] G. Bouchitté - M. Valadier, Integral representation of convex functionals on a space of measures, J. funct. Analysis, 80 (1988), 398-420. | Zbl

[16] G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes Math. Ser., 207, Longman, Harlow (1989).

[17] E. De Giorgi - L. Ambrosio, Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Natur. Rend., 82 (1988), 199-210. | fulltext bdim | fulltext EuDML

[18] E. De Giorgi - L. Ambrosio - G. Buttazzo, Integral representation and relaxation for functionals defined on measures, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Natur. Rend., 81 (1987), 7-13. | fulltext bdim | fulltext EuDML | Zbl

[19] L.C. Evans - R.F. Gariepy, Measure theory and fine properties of functions, Studies in advanced mathematics, CRC Press, Boca Raton, Florida, 1992.

[20] E. Giusti, Minimal surfaces and functions of bounded variation, Birkhäuser, Basel, 1984. | Zbl

[21] C. Goffman - J. Serrin, Sublinear functions of measure and variational integrals, Duke Math J., 31 (1964), 159-178. | Zbl

[22] M. Gori, On the definition on BV of a supremal functional, Preprint n. 2.449.1417 (October 2002) Università di Pisa.

[23] M. Gori - F. Maggi, On the lower semicontinuity of supremal functionals, ESAIM: COCV., 9 (2003), 135-143. | fulltext EuDML | Zbl

[24] M. Gori - F. Maggi, The common root of the geometric conditions in Serrin's lower semicontinuity theorem, to appear in Annali Mat. pura appl. | Zbl

[25] R. Jensen, Uniqueness of Lipchitz extensions: minimizing the sup norm of the gradient, Arch. Rational Mech. Anal., 123 (1993), 51-74. | Zbl

[26] R.T. Rockafellar - R.J-B. Wets, Variational Analysis, Die Grundlehren der mathematischen Wissenschaften 317, Springer-Verlag, Berlin, 1998.

[27] J. Serrin, On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc., 101 (1961), 139-167. | Zbl