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Integral characterization of functionals defined on spaces of BV functions. (English) Zbl 0439.49006


MSC:

49J99 Existence theories in calculus of variations and optimal control
49J20 Existence theories for optimal control problems involving partial differential equations
49N15 Duality theory (optimization)

Citations:

Zbl 0352.49005
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References:

[1] O. Caligaris - F. Ferro - P. Oliva , Sull’esistenza del minimo per problemi di calcolo delle variazioni relativi ad archi di variazione limitata , Boll. Un. Mat. Ital. , ( 5 ), 14-B ( 1977 ), pp. 340 - 369 .- MR 463998 | Zbl 0357.49002 · Zbl 0357.49002
[2] O. Caligaris - P. Oliva , Problemi di Bolza per archi di variazione limitata ed estensione di funzionali variazionali , Boll. Un. Mat. Ital. , ( 5 ), 14-B ( 1977 ), pp. 772 - 785 . MR 477947 | Zbl 0438.49014 · Zbl 0438.49014
[3] O. Caligaris - P. Oliva , Sulla caratterizzazione di problemi del calcolo delle variazioni per funzioni di variazione limitata , Boll. Un. Mat. Ital. , to appear. Zbl 0378.49009 · Zbl 0378.49009
[4] F. Ferro , Sul minimo di funzionali definiti sullo spazio delle funzioni di variazione limitata in n dimensioni , Ann. Mat. Pura Appl. , IV , 117 ( 1978 ), pp. 153 - 171 . Zbl 0396.49014 · Zbl 0396.49014
[5] F. Ferro , Functionals defined on functions of bounded variation in Rn and the Lebesgue area , SIAM J. Control Optimization , 16 , no. 5 (Sept. 1978 ). MR 505379 | Zbl 0382.46017 · Zbl 0382.46017
[6] F. Ferro , Variational functionals defined on spaces of BV functions and their dependence on boundary data , Ann. Mat. Pura Appl. , to appear. MR 565071 | Zbl 0434.46027 · Zbl 0434.46027
[7] J. Necas , Les méthodes directes en théorie des equations elliptiques , Masson et Cie , Paris ; Academia , Editeurs, Prague , 1967 . MR 227584 · Zbl 1225.35003
[8] R.T. Rockafellar , Convex analysis , Princeton Univ. Press , 1970 . MR 274683 | Zbl 0193.18401 · Zbl 0193.18401
[9] R.T. Rockafellar , Integrals which are convex functionals II , Pacific J. Math. , 39 ( 1971 ), pp. 439 - 469 . Article | MR 310612 | Zbl 0236.46031 · Zbl 0236.46031
[10] R.T. Rockafellar , Dual problem of Lagrange for arcs of bounded variation, in Calculus of variations and control theory , D. L. Russel ed., Academic Press , New York , 1976 ; Proc. of a Conference of the Mathematical Research Center, University of Wisconsin , Madison , September 1975 . MR 482468 | Zbl 0352.49005 · Zbl 0352.49005
[11] R.T. Rockefellar , Integral functionals, normal integrands and measurable selections, in Non linear operators and the Calculus of Variations , Lecture Notes in Mathematics , no. 543 , Springer-Verlag , Berlin - Heidelberg - New York , 1976 . MR 512209 | Zbl 0374.49001 · Zbl 0374.49001
[12] J. Serrin , On the definition and properties of certain variational integrals , Trans. Amer. Math. Soc. , 101 ( 1961 ), pp. 139 - 167 . MR 138018 | Zbl 0102.04601 · Zbl 0102.04601
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