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Théorème d'existence pour des problèmes variationnels non convexes

Published online by Cambridge University Press:  14 November 2011

J. P. Raymond
J. P. Raymond
Affiliation:
Laboratoire d'Analyse Numérique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
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Synopsis

On donne dans cet article un théorème d'existence de solutions lipschitziennes pour des problèmes du type:

où Ω est un ouvert convexe borné de ℝn, n ≧ 2, p ≧ 2, aucune hypothèse de convexité n'est faite sur g ou f. On étend de la sorte des ŕesultats d'existence obtenus en dimension 1.

where Ω is a bounded open convex subset of ℝn, n ≧ 2, p ≧ 2; we suppose no assumption of convexity on g or f. In this way we extend existence results proved in dimension 1.)

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 43 - 64
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Atteia, M.. Caractérisation des solutions geéneéralisées du probleme de Saint-Venant. Séminaire d'Analyse Numérique de Toulouse, Décembre 1983 (Toulouse: Université Paul Sabatier, 1983).Google Scholar
2Aubert, G.Tahraoui, R.. Theéorèmes d'existence pour des problèmes du calcul des variations. J. Differential Equations 33 (1979), 1–15.CrossRefGoogle Scholar
3Aubert, G.Tahraoui, R.. Theéorème d'existence en optimisation non convexe. Applicable Anal. 18, (1984), 75–100.CrossRefGoogle Scholar
4Ball, J.. Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63 (1977), 337–403.CrossRefGoogle Scholar
5Ekeland, I.. Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations. Publications Math, de 1'I.H.E.S. 77 (1977), 5–32.CrossRefGoogle Scholar
6Ekeland, I.Temam, R.. Analyse convexe et problème variationnels (Paris: Dunod, 1974).Google Scholar
7Gilbarg, D.Trudinger, N. S.. Elliptic Partial Differential Equations of Second Order (Berlin: Springer, 1977).CrossRefGoogle Scholar
8Gurtin, M. E.Temam, R.. On the anti-plane shear problem in finite elasticity. J. Elasticity 11 (1981), 197–206.CrossRefGoogle Scholar
9Hartman, P.Stampacchia, G.. On some non-linear elliptic differential-functional equations. Ada Math. 115 (1966), 271–310.Google Scholar
10Marcellini, P.. Proceedings of Congress on Mathematical theories of Optimization. Lecture Notes in Mathematics 979 (Berlin: Springer, 1982).Google Scholar
11Mascolo, E.Schianchi, R.. Existence theorems for non convex problems. J. Math. Pures Appl. 62 (1983), 349–359.Google Scholar
12Raymond, J. P.. Thèse 3° cycle (Toulouse—U.P.S., 1982).Google Scholar
13Raymond, J. P.. C.N.S. d'existence de solutions en calcul des variations. Ann. Inst. H. Poincare, Analyse non linéaire (à paraître).Google Scholar
14Raymond, J. P.. Champs hamiltoniens, Relaxation et Existence de solutions en calcul des variations. J. Differential Equations (à paraître).Google Scholar
15Saks, S.. Theory of the Integral (New York: Hafner, 1937).Google Scholar
16Stampacchia, G.. On some regular Multiple Integral Problems in the Calculus of Variations. Comm. Pure Appl. Math. 16 (1963), 383–421.CrossRefGoogle Scholar
17Stampacchia, G.. Equations elliptiques du second ordre à coefficients discontinue (Montreal: Université de Montréal, n° 16, 1966).Google Scholar
18Yosida, K.. Functional Analysis (Berlin: Springer, 1978).CrossRefGoogle Scholar