Relaxation for a class of nonconvex functionals defined on measures

Guy Bouchitté; Giuseppe Buttazzo

Annales de l'I.H.P. Analyse non linéaire (1993)

  • Volume: 10, Issue: 3, page 345-361
  • ISSN: 0294-1449

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Bouchitté, Guy, and Buttazzo, Giuseppe. "Relaxation for a class of nonconvex functionals defined on measures." Annales de l'I.H.P. Analyse non linéaire 10.3 (1993): 345-361. <http://eudml.org/doc/78306>.

@article{Bouchitté1993,
author = {Bouchitté, Guy, Buttazzo, Giuseppe},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {lower semicontinuous envelope; measures with finite variation},
language = {eng},
number = {3},
pages = {345-361},
publisher = {Gauthier-Villars},
title = {Relaxation for a class of nonconvex functionals defined on measures},
url = {http://eudml.org/doc/78306},
volume = {10},
year = {1993},
}

TY - JOUR
AU - Bouchitté, Guy
AU - Buttazzo, Giuseppe
TI - Relaxation for a class of nonconvex functionals defined on measures
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1993
PB - Gauthier-Villars
VL - 10
IS - 3
SP - 345
EP - 361
LA - eng
KW - lower semicontinuous envelope; measures with finite variation
UR - http://eudml.org/doc/78306
ER -

References

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  1. [1] L. Ambrosio and 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. Zbl0721.49041
  3. [3] G. Bouchitté and G. Buttazzo, New Lower Semicontinuity Results for non Convex Functionals defined on Measures, Nonlinear Anal., Vol. 15, 1990, pp. 679-692. Zbl0736.49007
  4. [4] G. Bouchitté and G. Buttazzo, Integral Representation of Nonconvex Functionals defined on Measures, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear). Zbl0757.49012
  5. [5] G. Bouchitté and M. Valadier, Integral Representation of Convex Functionals on a Space of Measures, J. Funct. Anal., Vol. 80, 1988, pp. 398-420. Zbl0662.46009
  6. [6] G. Bouchitté and 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 deJ. J. Moreau, Bordas, Paris, 1989, pp. 123-149. Zbl0704.49017
  7. [7] G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes Math. Ser., Vol. 207, Longman, Harlow, 1989. Zbl0669.49005
  8. [8] G. Buttazzo and G. Dal Maso, On Nemyckii Operators and Integral Representation of Local Functionals. Rend. Mat., Vol. 3, 1983, pp. 491-509. Zbl0536.47027
  9. [9] E. De Giorgi, L. Ambrosio and 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
  10. [10] F. Demengel and R. Temam, Convex Functions of Measures and Applications, Indiana Univ. Math. J., Vol. 33, 1984, pp. 673-709. Zbl0581.46036
  11. [11] N. Dunford and J.T. Schwartz, Linear Operators, Interscience Publishers Inc., New York, 1957. Zbl0084.10402
  12. [12] C. Goffman and J. Serrin, Sublinear Functions of Measures and Variational Integrals, Duke Math. J., Vol. 31, 1964, pp. 159-178. Zbl0123.09804
  13. [13] F. Hiai, Representation of Additive Functionals on Vector Valued normed Kothe Spaces, Kodai Math. J., Vol. 2, 1979, pp. 300-313. Zbl0431.46025
  14. [14] A.D. Ioffe, On Lower Semicontinuity of Integral Functionals I. II, SIAM J. Control Optim., Vol. 15, 1977, pp. 521-538 and 991-1000. Zbl0361.46037
  15. [15] 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. Zbl0159.43804
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  17. [17] M. Valadier, Closedness in the Weak Topology of the Dual Pair L1, C, J. Math. Anal. Appl., Vol. 69, 1979, pp. 17-34. Zbl0412.46040

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