Geodesic
Approximation De Fonctions Convexes Sur Un Espace De Mesures Et Applications
Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 392-413

Voir la notice de l'article provenant de la source Cambridge University Press

In the first part of this article we recall the definition and a few basic properties of convex functionals defined on a space of bounded measures. In the second part we show several results of approximation of the following type: Although a measure μ cannot be approximated in the sense of the norm by smooth functions, we can find an appropriate sequence of smooth functions which converge weakly to the measure μ, the corresponding value of the functional converging to the value of the functional at μ.This article is part of a series on the existence theory of solution of variational problems of mechanics (perfect plasticity), which is based on a systematic utilization of the methods of convex analysis and the calculus of variations.
DOI : 10.4153/CMB-1982-058-7
Mots-clés : 49A99, 28A99 
Temam, R. Approximation De Fonctions Convexes Sur Un Espace De Mesures Et Applications. Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 392-413. doi: 10.4153/CMB-1982-058-7
@article{10_4153_CMB_1982_058_7,
     author = {Temam, R.},
     title = {Approximation {De} {Fonctions} {Convexes} {Sur} {Un} {Espace} {De} {Mesures} {Et} {Applications}},
     journal = {Canadian mathematical bulletin},
     pages = {392--413},
     year = {1982},
     volume = {25},
     number = {4},
     doi = {10.4153/CMB-1982-058-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-058-7/}
}
TY  - JOUR
AU  - Temam, R.
TI  - Approximation De Fonctions Convexes Sur Un Espace De Mesures Et Applications
JO  - Canadian mathematical bulletin
PY  - 1982
SP  - 392
EP  - 413
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-058-7/
DO  - 10.4153/CMB-1982-058-7
ID  - 10_4153_CMB_1982_058_7
ER  - 
%0 Journal Article
%A Temam, R.
%T Approximation De Fonctions Convexes Sur Un Espace De Mesures Et Applications
%J Canadian mathematical bulletin
%D 1982
%P 392-413
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-058-7/
%R 10.4153/CMB-1982-058-7
%F 10_4153_CMB_1982_058_7

[1] 1. Bourbaki, N., Topologie Générale, Livre III, Hermann, Paris (1964). Google Scholar

[2] 2. Bourbaki, N., Intégration, Livre VI, Hermann, Paris (1965). Google Scholar

[3] 3. Brézis, H., Intégrales Convexes dans les Espaces de Sobolev, Israel J. Math., 13 (1972), p.9-23. Google Scholar

[4] 4. Ekeland et, I. Temam, R., Analyse Convexe et Problèmes Variationnels, Dunod-Gauthier-Villars, Paris (1974); North-Holland, Amsterdam (1976) (en anglais). Google Scholar

[5] 5. Giusti, E., Minimal Surfaces and functions of Bounded Variation, Notes de cours rédigées par G. H.Williams, Department of Mathematics, Australian National University, Canberra, 10 (1977). Google Scholar

[6] 6. Goffman, C. and Serrin, J., Sublinear Functions of Measures and Variational Integrals, Duke Math. J., 31 (1964), p. 159-178. Google Scholar

[7] 7. Krasnoselskii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, London (1964). Google Scholar

[8] 8. Matthies, H., Strang, G., and Christiansen, E., The saddle point of a differential program, in "Energy methods in finite element analysis," Glowinski, R., Rodin, E., Zienkiewicz, O. C., éditeurs, John Wiley, New York, 1979. Google Scholar

[9] 9. Moreau, J. J., Fonctionnelles Convexes, Séminaire Equations aux Dérivées Partielles, Collège de France (1966). Google Scholar

[10] 10. Rockafellar, R. T., Convex Analysis Princeton University Press, Princeton (1970). Google Scholar

[11] 11. Rockafellar, R. T., Integral Functionals, normal integrands and measurable selections, dans Nonlinear Operators and the Calculus of Variations, Lecture Notes in Math., vol. 543, Springer-Verlag, Heidelberg (1976). Google Scholar

[12] 12. Rockafellar, R. T., Integral which are convex functionals I and II, Pacific J. Math., 24 (1966), p. 525-539 et 39 (1971), p. 439-469. Google Scholar

[13] 13. Suquet, P., Existence et régularité des solutions des équations de la plasticité parfaite, Thèse de 3ème cycle, Université de Paris VI (1978) et C.R.Ac.Sc. Paris, 286, Série D, (1978), p. 1201-1204. Google Scholar

[14] 14. Strang et, G. Temam, R., Functions of bounded deformation, Arch. Rat. Mech. Anal., 75 (1980) p. 7-21. Google Scholar

[15] 15. Strang et, G. Temam, R., Duality and Relaxation in plasticity. Journal de Mécanique, 19 (1980) p. 493-527. Google Scholar

[16] 16. Temam, R., Applications de l' Analyse Convexe au Calcul des Variations, dans Nonlinear Operator and the Calculus of Variations, Lecture Notes in Math., vol. 543, Springer-Verlag, Heidelberg (1976). Google Scholar

[17] 17. Temam, R., Mathematical Problems in Plasticity, dans "Complementarity Problems and variational Inequalities" Gianessi, F., Cottle, , Lions, J. L., editors, John Wiley, New York, 1979. Google Scholar

[18] 18. Temam, R., Existence theorems for the variational problems of plasticity, dans Nonlinear problems of Analysis in Geometry and Mechanics, Atteia Bancel et Gumowski, éd., Pitman, London, 1981. Google Scholar

[19] 19. Temam, R., On the continuity of the trace of vector functions with bounded deformation, Applicable Analysis, 11 (1981), p. 291-302. Google Scholar

Cité par Sources :