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Integral representation of nonconvex functionals defined on measures

G. Bouchitté; G. Buttazzo

Annales de l'I.H.P. Analyse non linéaire (1992)

  • Volume: 9, Issue: 1, page 101-117
  • ISSN: 0294-1449

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Bouchitté, G., and Buttazzo, G.. "Integral representation of nonconvex functionals defined on measures." Annales de l'I.H.P. Analyse non linéaire 9.1 (1992): 101-117. <http://eudml.org/doc/78268>.

@article{Bouchitté1992,
author = {Bouchitté, G., Buttazzo, G.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {integral representation; nonconvex functionals; measures with bounded variation; lower semicontinuity result},
language = {eng},
number = {1},
pages = {101-117},
publisher = {Gauthier-Villars},
title = {Integral representation of nonconvex functionals defined on measures},
url = {http://eudml.org/doc/78268},
volume = {9},
year = {1992},
}

TY - JOUR
AU - Bouchitté, G.
AU - Buttazzo, G.
TI - Integral representation of nonconvex functionals defined on measures
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 1
SP - 101
EP - 117
LA - eng
KW - integral representation; nonconvex functionals; measures with bounded variation; lower semicontinuity result
UR - http://eudml.org/doc/78268
ER -

References

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  1. [1] L. Ambrosio & G. Buttazzo, Weak lower semicontinuous envelope of functionals defined on a space of measures. Ann. Mat. Pura Appl., Vol. 150, 1988, pp. 311-340. Zbl0648.49009
  2. [2] G. Bouchitté, Représentation intégrale de fonctionnelles convexes sur un espace de mesures. Ann. Univ. Ferrara, Vol. 33, 1987, pp. 113-156. Zbl0721.49041MR958390
  3. [3] G. Bouchitté & G. Buttazzo, New lower semicontinuity results for non convex functionals defined on measures. Nonlinear Anal., Vol. 15, 7, 1990, pp. 679-692. Zbl0736.49007
  4. [4] G. Bouchitié & M. Valadier, Integral representation of convex functionals on a space of measures. J. Funct. Anal., Vol. 80, 1988, pp. 398-420. Zbl0662.46009
  5. [5] G. Bouchitté & M. Valadier, Multifonctions s.c.i. et régularisée s.c.i. essentielle. Proceedings "Congrès Franco-Québécois d'Analyse Non linéaire Appliquée", Perpignan, June 22–26, 1987, in "Analyse Non linéaire - Contribution en l'Honneur de J. J. Moreau", Bordas, Paris, 1989, pp. 123-149. Zbl0704.49017
  6. [6] G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Pitman Res. Notes Math. Ser., Vol. 207, Longman, Harlow, 1989. Zbl0669.49005MR1020296
  7. [7] G. Buttazzo & G. Dal Maso, On Nemyckii operators and integral representation of local functionals. Rend. Mat., Vol. 3, 1983, pp. 491-509. Zbl0536.47027
  8. [8] E. De Giorgi, L. Ambrosio & G. Buttazzo, Integral representation and relaxation for functionals defined on measures. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., Vol. 81, 1987, pp. 7-13. Zbl0713.49018
  9. [9] F. Demengel & R. Temam, Convex functions of measures and applications. Indiana Univ. Math. J., 33, 1984, pp. 673-709. Zbl0581.46036
  10. [10] N. Dunford & J.T. Schwartz, Linear Operators. Interscience Publishers Inc., New York, 1957. Zbl0084.10402
  11. [11] C. Goffman & J. Serrin, Sublinear functions of measures and variational integrals. Duke Math. J., Vol. 31, 1964, pp. 159-178. Zbl0123.09804
  12. [12] F. Hiai, Representation of additive functionals on vector valued normed Köthe spaces. Kodai Math. J., Vol. 2, 1979, pp. 300-313. Zbl0431.46025MR553237
  13. [13] A.D. Ioffe, On lower semicontinuity of integral functionals I. II.SIAM J. Control Optim., Vol. 15, 1977, pp. 521-538 nd 991-1000. Zbl0361.46037MR637234
  14. [14] R.T. Rockafellar, Integrals which are convex functionals I. II. Pacific J. Math., Vol. 24, 1968, pp. 525-539 and Vol. 39, 1971, pp. 439-469. Zbl0159.43804MR236689
  15. [15] R.T. Rockafellar, Convex Analysis . Princeton University Press, Princeton, 1972. Zbl0193.18401MR1451876
  16. [16] M. Valadier, Closedness in the weak topology of the dual pair L1, C. J. Math. Anal. Appli., Vol. 69, 1979, pp. 17-34. Zbl0412.46040MR535279

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