Integral representation and relaxation of convex local functionals on BV(Ω)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 20 (1993) no. 4, pp. 483-533.
@article{ASNSP_1993_4_20_4_483_0,
     author = {Bouchitt\'e, Guy and Dal Maso, Gianni},
     title = {Integral representation and relaxation of convex local functionals on $BV(\Omega )$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {483--533},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 20},
     number = {4},
     year = {1993},
     zbl = {0802.49008},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1993_4_20_4_483_0/}
}
TY  - JOUR
AU  - Bouchitté, Guy
AU  - Dal Maso, Gianni
TI  - Integral representation and relaxation of convex local functionals on $BV(\Omega )$
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1993
SP  - 483
EP  - 533
VL  - 20
IS  - 4
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1993_4_20_4_483_0/
LA  - en
ID  - ASNSP_1993_4_20_4_483_0
ER  - 
%0 Journal Article
%A Bouchitté, Guy
%A Dal Maso, Gianni
%T Integral representation and relaxation of convex local functionals on $BV(\Omega )$
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1993
%P 483-533
%V 20
%N 4
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1993_4_20_4_483_0/
%G en
%F ASNSP_1993_4_20_4_483_0
Bouchitté, Guy; Dal Maso, Gianni. Integral representation and relaxation of convex local functionals on $BV(\Omega )$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 20 (1993) no. 4, pp. 483-533. http://archive.numdam.org/item/ASNSP_1993_4_20_4_483_0/

[1] G. Alberti, Rank one properties for derivatives of functions with bounded variation. Proc. Roy. Soc. Edinburgh Sect. A, to appear. | MR | Zbl

[2] G. Alberti - G. Buttazzo, Integral representation of functionals defined on Sobolev spaces. Composite media and homogenization theory, 1-12 Birkhäuser, Boston, 1991. | MR | Zbl

[3] G. Anzellotti, Pairing between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl.(4) 135 (1983), 293-318. | MR | Zbl

[4] G. Anzellotti, Traces of bounded vectorfields and the divergence theorem. Preprint Univ. Trento, 1983. | MR

[5] H. Attouch, Variational convergence for functions and operators. Pitman, London, 1984. | MR | Zbl

[6] G. Bouchitié, Représentation intégrale de fonctionelles convexes sur un espace de mesures. II. Cas de l'épi-convergence. Ann. Univ. Ferrara Sez. VII (N.S.) 33 (1987), 113-156. | MR | Zbl

[7] G. Bouchitté - M. Valadier, Integral representation of convex functionals on a space of measures. J. Funct. Anal. 80 (1988), 398-420. | MR | Zbl

[8] G. Buttazzo, Semicontinuity, relaxation and integral representation problems in the calculus of variations. Pitman Res. Notes in Math., Longman, Harlow, 1989. | Zbl

[9] G. Buttazzo - G. Dal Maso, Γ-limits of integral functionals. J. Analyse Math. 37 (1980), 145-185. | Zbl

[10] G. Buttazzo - G. Dal Maso, Integral representation and relaxation of local functionals. Nonlinear Anal. 9 (1985), 515-532. | MR | Zbl

[11] G. Buttazzo - L. Freddi, Functionals defined on measures and applications to non equi-uniformly elliptic problems. Ann. Mat. Pura Appl. (4) 159 (1991), 133-149. | MR | Zbl

[12] L. Carbone - C. Sbordone, Some properties of Γ-limits of integral functionals. Ann. Mat. Pura Appl. (4) 122 (1979), 1-60. | Zbl

[13] M. Carriero - E. Pascali, Γ-convergenza di integrali non negativi maggiorati da funzionali del tipo dell'area. Ann. Univ. Ferrara Sez. VII (N.S.) 24 (1978), 51-64. | Zbl

[14] C. Castaing - M. Valadier, Convex analysis and measurable multifunctions. Lecture Notes in Math. 580, Springer-Verlag, Berlin, 1977. | MR | Zbl

[15] G. Dal Maso, Integral representation on BV(Ω) of Γ-limits of variational integrals. Manuscripta Math. 30 (1980), 387-416. | Zbl

[16] G. Dal Maso - L. Modica, A general theory of variational functionals. Topics in functional analysis (1980-1981), 149-221, Quaderni Scuola Norm. Sup. Pisa, Pisa, 1981. | MR | Zbl

[17] E. De Giorgi, Sulla convergenza di alcune successioni di integrali del tipo dell'area. Rend. Mat (6) 8 (1975), 277-294. | MR | Zbl

[18] E. De Giorgi - T. Franzoni, Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58 (1975), 842-850, and Rend. Sem. Mat. Brescia 3 (1979), 63-101. | MR | Zbl

[19] N. Dunford - J.T. Schwartz, Linear operators. Interscience, New York, 1957. | Zbl

[20] I. Ekeland - R. Temam, Convex analysis and variational problems. North-Holland, Amsterdam, 1976. | MR | Zbl

[21] A. Gavioli, Necessary and sufficient conditions for the lower semicontinuity of certain integral functionals. Ann. Univ. Ferrara Sez. VII (N.S.), 34 (1988), 219-236. | MR | Zbl

[22] M. Giaquinta - G. Modica - J. Soucek, Functionals with linear growth in the calculus of variations. I. Comment. Math. Univ. Carolin. 20 (1979), 143-156. | MR | Zbl

[23] E. Giusti, Minimal surfaces and functions of bounded variation. Birkhäuser, Boston, 1984. | MR | Zbl

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

[25] P. Marcellini - C. Sbordone, Semicontinuity problems in the calculus of variations. Nonlinear Anal. 4 (1980), 241-257. | MR | Zbl

[26] V.G. Maz'Ya, Sobolev spaces. Springer-Verlag, Berlin, 1985. | MR | Zbl

[27] R.T. Rockafellar, Convex Analysis. Princeton University Press, Princeton, 1970. | MR | Zbl

[28] R.T. Rockafellar, Convex integral functionals and duality. Contributions to Nonlinear Functional Analysis, 215-236. Academic Press, New York, 1971. | MR | Zbl

[29] R.T. Rockafellar, Conjugate duality and optimization. CBMS-NSF Regional Conf. Ser. in Appl. Math. 16, SIAM, Philadelphia, 1974. | MR | Zbl

[30] C. Sbordone, Su alcune applicazioni di un tipo di convergenza variazionale. Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4) 2 (1975), 617-638. | Numdam | MR | Zbl

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

[32] L.M. Simon, Lectures on geometric measure theory. Proc. of the Centre for Mathematical Analysis (Canberra), Australian National University, 3, 1983. | MR | Zbl

[33] R. Temam, Problèmes mathematiques en plasticité. Gauthier-Villars, Paris, 1983. | MR | Zbl

[34] M. Valadier, Multi-applications measurables à valeurs convexes compactes. J. Math. Pures Appl. 50 (1971), 265-297. | MR | Zbl

[35] A.I. Vol'Pert - S.I. Hudjaev, Analysis in classes of discontinuous functions and equations of mathematical physics. Martinus Nijhoff Publishers, Dordrecht, 1985. | MR | Zbl