On the lower semicontinuity of supremal functionals

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 9, Issue , 2003, Pages 135-143

  Gori, Michele ^a   Maggi, Francesco ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Calculus of Variations; Lower semicontinuity; Mazur s lemma; Supremal functionals

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GRADIENT METHODS; INTEGRAL EQUATIONS; NUMERICAL METHODS; THEOREM PROVING;

ANALOGOUS THEORY; LEVEL CONVEXITY; LOWER SEMICONTINUITY; MAZUR'S LEMMA; SUPREMAL FUNCTIONALS;

PROBLEM SOLVING;

EID: 12844250580     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2003005     Document Type: Article

References (21)

1. E. Acerbi, G. Buttazzo and F. Prinari, The class of functionals which can be represented by a supremum. J. Convex Anal. 9 (to appear).
2. L. Ambrosio, New lower semicontinuity results for integral functionals. Rend. Accad. Naz. Sci. XL 11 (1987) 1-42.
3. x F(x, f (x), f'(x)). Ark. Mat. 6 (1965) 33-53.
4. G. Aronsson, Extension of functions satisfying Lipschitz conditions. Ark. Mat. 6 (1967) 551-561.
5. x F(x, f (x), f'(x)) II. Ark. Mat. 6 (1969) 409-431.
6. x F(x, f (x), f(x)) III. Ark. Mat. 7 (1969) 509-512.
7. E.N. Barron, R.R. Jensen and C.Y. Wang, Lower semicontinuity of L^ functionals. Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001) 495-517.
8. E.N. Barron and W. Liu, Calculus of variations in L^. Appl. Math. Optim. 35 (1997) 237-263.
9. G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Longman, Harlow, Pitman Res. Notes Math. Ser. 207 (1989).
10. L. Carbone and C. Sbordone, Some properties of T-limits of integral functionals. Ann. Mat. Pura Appl. 122 (1979) 1-60.
11. G. Dal Maso, Integral representation on BV(D) of T-limits of variational integrals. Manuscripta Math. 30 (1980) 387-416.
12. E. De Giorgi, Teoremi di semicontinuita nel calcolo delle variazioni. Istituto Nazionale di Alta Matematica, Roma (1968).
13. E. De Giorgi, G. Buttazzo and G. Dal Maso, On the lower semicontinuity of certain integral functionals. Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Natur., Rend. 74 (1983) 274-282.
14. G. Eisen, A counterexample for some lower semicontinuity results. Math. Z. 162 (1978) 241-243.
15. I. Fonseca and G. Leoni, Some remarks on lower semicontinuity. Indiana Univ. Math. J. 49 (2000) 617-635.
16. I. Fonseca and G. Leoni, On lower semicontinuity and relaxation. Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 519-565.
17. 1. Differential Integral Equations (to appear).
18. M. Gori and P. Marcellini, An extension of the Serrin’s lower semicontinuity theorem. J. Convex Anal. 9 (2002) 1-28.
19. A.D. Ioffe, On lower semicontinuity of integral functionals. SIAM J. Control Optim. 15 (1977) 521-538.
20. C.Y. Pauc, La meéthode méetrique en calcul des variations. Hermann, Paris (1941).
21. J. Serrin, On the definition and properties of certain variational integrals. Trans. Amer. Math. Soc. 101 (1961) 139-167.