Régularité de la solution d'un problème variationnel
Annales de l'I.H.P. Analyse non linéaire, Volume 9 (1992) no. 1, p. 51-99
@article{AIHPC_1992__9_1_51_0,
     author = {Tahraoui, Rabah},
     title = {R\'egularit\'e de la solution d'un probl\`eme variationnel},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {9},
     number = {1},
     year = {1992},
     pages = {51-99},
     zbl = {0757.49015},
     mrnumber = {1151467},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPC_1992__9_1_51_0}
}
Tahraoui, R. Régularité de la solution d'un problème variationnel. Annales de l'I.H.P. Analyse non linéaire, Volume 9 (1992) no. 1, pp. 51-99. http://www.numdam.org/item/AIHPC_1992__9_1_51_0/

[1] J.L. Ericksen, Equilibrium of Bars, J. Elasticity, vol. 5, 1975, p. 191-201. | MR 471528 | Zbl 0324.73067

[2] J.L. Knowles, On Finite Anti-Plane Shear for Incompressible Elastic Materials, J. Austral. Math. Soc., Serie B 19, 1976, p. 400-415. | MR 475116 | Zbl 0363.73045

[3] R.L. Fosdick et R.D. James, The Elastica and the Problem of the Pure Bending for Non Convex Stored Energy Function, J. Elasticity, vol. 11, 1981, p. 165-186. | MR 614373 | Zbl 0481.73018

[4] J.M. Ball, Convexity Conditions and Existence Theorems in Non Linear Elasticity, Arch. Rational mech. Anal., vol. 63, 1977, p. 337-403. | MR 475169 | Zbl 0368.73040

[5] P.G. Ciarlet, Mathematical Elasticity, Publication du Laboratoire d'Analyse Numérique, Université Paris-VI, Part I, n°A86007.

[6] G. Aubert et R. Tahraoui, Théorèmes d'existence pour des problèmes du calcul des variations du type Inf ∫L0 f (x, u') dx et Inf ∫L0 f(x, u, u') dx, J. Differential Equations, vol. 33, 1979, p. 1-15. | MR 540812 | Zbl 0404.49001

[7] I. Ekeland, Discontinuité de champs hamiltoniens et existence de solutions optimales en calcul des variations, Inst. Hautes Études Sci. Publi. Math., vol. 47, 1977, p. 5-32. | Numdam | MR 493584 | Zbl 0447.49015

[8] G. Aubert et R. Tahraoui, Théorèmes d'existence en optimisation non convexe, Appl. Anal., vol. 18, 1984, p. 75-100. | MR 762866 | Zbl 0522.49002

[9] P. Marcellini, A Relation Between Existence of Minima for Non Convex Integrals and Uniqueness for Non Strictly Convex Integrals of the Calculus of Variations, Proceeding of Congress on Mathematical Theories of Optimization; Lecture Notes in Mathematics, n° 979, p. 216-231 (Berlin : Springer, 1983). | MR 713812 | Zbl 0505.49009

[10] J.P. Raymond, Théorème d'existence pour des problèmes variationnels non convexes, Proceeding of the Royal Society of Edinburgh, vol. 107 A, 1987, p. 43-64. | MR 918892 | Zbl 0628.49006

[11] E. Mascolo et R. Schianchi, Existence Theorems in the Calculus of Variations, J. Differential Equations, vol. 67, n° 2, 1987. | MR 879692

[12] E. Mascolo et R. Schianchi, Existence Theorems for Non Convex Problems, J. Math. Pures Appl., vol. 62, 1983, p. 349-359. | MR 718948 | Zbl 0522.49001

[13] R. Tahraoui, Théorèmes d'existence en calcul des variations et applications à l'élasticité non linéaire, Proceeding of the Royal Society of Edinburgh, vol. 109 A, 1988, p. 51- 78. | MR 952329 | Zbl 0681.49004

[14] P. Hartman et G. Stampacchia, On Some Non-Linear Elliptic Differential-functional Equations, Acta Mathematica, vol. 115, 1966, p. 271-310. | MR 206537 | Zbl 0142.38102

[15] J.P. Aubin et I. Ikeland, Applied Nonlinear Analysis, Edit John Wiley and Sons, New York, 1984. | MR 749753 | Zbl 0641.47066

[16] G. Aubert et R. Tahraoui, Sur quelques résultats d'existence en optimisation non convexe, C. R. Acad. Sci. Paris, t. 297, série I, 1983, p. 287-290. | MR 734570 | Zbl 0534.49004

[17] R.T. Rockafellar, Convex Analysis, Princeton University Press. | MR 1451876 | Zbl 0932.90001

[18] G. Stampacchia, On Some Regular Multiple Integral Problems in the Calculus of Variations, C.P.A.M., vol. XVI, 1963, p. 383-421. | MR 155209 | Zbl 0138.36903

[19] A. Visintin, Strong Convergence Results Related to Strict Convexity, Com. in partial differential equations, vol. 9, (5), 1984, p. 439-466. | MR 741216 | Zbl 0545.49019

[20] R. Tahraoui, Régularité de la solution d'un problème variationnel et application, C. R. Acad. Sci. Paris, t. 305, série I, 1987, p. 327-330. | MR 909558 | Zbl 0639.49003

[21] G. Aubert et R. Tahraoui, Sur quelques résultats d'existence en optimisation non convexe, C. R. Acad. Sci. Paris, t. 297, série I, 1983, p. 287-290. | MR 734570 | Zbl 0534.49004

[22] R. Tahraoui, Travail en préparation.

[23] I. Ekeland et R. Temam, Analyse convexe et problèmes variationnels, Dunod, Paris, 1974. | MR 463993 | Zbl 0281.49001

[24] P. Marcellini, Alcune osservazioni sull' esistenza del minimo di integrali del calcolo delle variazioni senza ipotesi di convessità, Rendiconti Mat., t. 13, 1980, p. 271-281. | Zbl 0454.49015

[25] P. Marcellini, Regularity of Minimizers of integrals of the calculus of variations with non standard growth conditions, Arch. Rat. Mech. An., vol. 105, n° 3, 1989, p. 267-284. | MR 969900 | Zbl 0667.49032

[26] P. Marcellini, Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals, Manuscripta Math., vol. 51, 1985, p. 1-28. | MR 788671 | Zbl 0573.49010

[27] R. Tahraoui, Régularité de la solution d'un problème variationnel, Cahiers du Ceremade, n° 9006.