A remark on serrin's theorem

Nonlinear Differential Equations and Applications

Volumn 13, Issue 4, 2006, Pages 425-433

  Fusco, Nicola ^a   Gori, Michele ^b   Maggi, Francesco ^c  

^a Dipartimento di Matematica e Applicazioni   (Italy)

^b UNIVERSITY OF PISA   (Italy)

^c Dipartimento di Matematica U Dini   (Italy)

Author keywords

Calculus of Variations; Convexity; Demicoercivity; Lower semicontinuity

Indexed keywords

EID: 34147181590     PISSN: 10219722     EISSN: 14209004     Source Type: Journal    
DOI: 10.1007/s00030-006-4018-8     Document Type: Article

References (20)

1. L. AMBROSIO, New lower semicontinuity results for integral functionals, Rend. Accad. Naz. Sci. XL, 11 (1987), 1-42.
2. L. AMBROSIO, N. FUSCO and D. PALLARA, Functions of bounded variation and free discontinuity problems, Oxford University Press, Oxford, 2000.
3. G. ANZELLOTTI, G. BUTTAZZO and G. DAL MASO, Dirichlet problem for demi-coercive functionals, Nonlinear Anal. 10 (1986), 603-613.
4. J. BENOIST and J. B. HIRIART-URRUTY, What is the subdifferential of the closed convex hull of a function?, SIAM J. Math. Anal. 27 (1996), 1661-1679.
5. G. BUTTAZZO, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes Math. Ser. 207, Longman, Harlow, 1989.
6. G. DAL MASO, Integral representation on BV(Ω) of F-limits of variational integrals, Manuscripta Math. 30 (1980), 387-416.
7. 1(div; Ω) and its applications to lower semicontinuity, Calc. Var. Partial Differential Equations. 19 (2004), 23-51.
8. E. DE GIORGI, Teoremi di semicontinuitá nel calcolo dette variazioni, Istituto Nazionale di Alta Matematica, Roma, 1968-1969.
9. 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.
10. G. EISEN, A counterexample for some lower semicontinuity results, Math. Z. 162 (1978), 241-243.
11. I. FONSECA and G. LEONI, On lower semicontinuity and relaxation, Proc. Roy. Soc. Edinburgh. 131A (2001), 519-565.
12. 1-lower semicontinuity in BV, J. Convex Anal. 12 (2005), 173-185.
13. 1- lower semicontinuity for integral functionals in BV, Manuscripta Math. 112 (2003), 313-323.
14. M. GORI and F. MAGGI, The common root of the geometric conditions in Serrin's lower semicontinuity theorem, Ann. Mat. Pura Appl. 184(4) (2005), 95-114.
15. 1, Differential Integral Equations. 16 (2003), 51-76.
16. M. GORI and P. MARCELLINI, An extension of the Serrin's lower semicontinuity theorem, J. Convex Analysis. 9 (2002), 475-502.
17. A. D. IOFFE, On lower semicontinuity of integral functional, SIAM J. Control Optim. 15 (1977), 521-538.
18. F. MAGGI, On the relaxation on BV of certain non coercive integral functionals, J. Convex Anal. 10 (2003), 477-489.
19. C. Y. PAUC, La méthode métrique en calcul des variations. Paris, Hermann, 1941.
20. J. SERRIN, On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc. 101 (1961), 139-167.