On a classical problem of the calculus of variations without convexity assumptions

A. Cellina; G. Colombo

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 2, page 97-106
  • ISSN: 0294-1449

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Cellina, A., and Colombo, G.. "On a classical problem of the calculus of variations without convexity assumptions." Annales de l'I.H.P. Analyse non linéaire 7.2 (1990): 97-106. <http://eudml.org/doc/78218>.

@article{Cellina1990,
author = {Cellina, A., Colombo, G.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {2},
pages = {97-106},
publisher = {Gauthier-Villars},
title = {On a classical problem of the calculus of variations without convexity assumptions},
url = {http://eudml.org/doc/78218},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Cellina, A.
AU - Colombo, G.
TI - On a classical problem of the calculus of variations without convexity assumptions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 2
SP - 97
EP - 106
LA - eng
UR - http://eudml.org/doc/78218
ER -

References

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  1. [A-T1] G. Aubert and R. Tahraoui, Théorèmes d'existence pour des problèmes du calcul des variations du type : Inf ∫L0 f (x, u' (x)) dx et Inf ∫L0 f (x, u (x), u' (x)) dx, J. Diff. Eq., Vol. 33, 1979, pp. 1-15. Zbl0404.49001MR540812
  2. [A-T2] G. Aubert and R. Tahraoui, Théorèmes d'existence en optimisation non convexe, Appl. Anal., Vol. 18, 1984, pp. 75-100. Zbl0522.49002MR762866
  3. [C-V] C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math., Springer-Verlag, Berlin, 1977. Zbl0346.46038MR467310
  4. [Ce1] L. Cesari, An existence theorem without convexity conditions, S.I.A.M. J. Control, Vol. 12, 1974, pp. 319-331. Zbl0255.49008MR383179
  5. [Ce2] L. Cesari, Optimization-Theory and Applications, Springer-Verlag, New York, 1983. Zbl0506.49001MR688142
  6. [C] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983. Zbl0582.49001MR709590
  7. [E] I. Ekeland, Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations, Publications Mathématiques de l'I.H.E.S., Vol. 47, 1977, pp. 5-32. Zbl0447.49015MR493584
  8. [E-T] I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. Zbl0322.90046MR463994
  9. [M1] P. Marcellini, Alcune osservazioni sull'esistenza del minimo di integrali del calcolo delle variazioni senza ipotesi di convessità, Rend. di Matem., (2), Vol. 13, 1980, pp. 271-281. Zbl0454.49015
  10. [M2] P. Marcellini, A Relation Between Existence of Minima for Non Convex Integrals and Uniqueness for Non Strictly Convex Integrals of the Calculus of Variations, Proc. of Congress on Mathematical Theories of Optimization, Zbl0505.49009
  11. S. Margherita Ligure, J.P. Cecconi and T. Zolezzi Ed., Lecture Notes in Math., Vol. 979, Springer-Verlag, Berlin, 1983. Zbl0499.00010MR713802
  12. [M3] P. Marcellini, Some Remarks on Uniqueness in the Calculus of Variations, Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. IV, Pitman, Boston, 1984. Zbl0521.49005MR716516
  13. [O] C. Olech, Integrals of Set-Valued Functions and Linear Optimal Control Problems, Colloque sur la Théorie Mathématique du Contrôle Optimal, C.B.R.M., Vander, Louvain, 1970, pp. 109-125. Zbl0261.49038
  14. [R] J.P. Raymond, Conditions nécessaires et suffisantes d'existence de solutions en calcul des variations, Ann. Inst. H. Poincaré, Analyse non linéaire, Vol. 4, 1987, pp. 169-202. Zbl0641.49012MR886931

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