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A relation between existence of minima for non convex integrals and uniqueness for non strictly convex integrals of the calculus of variations

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Mathematical Theories of Optimization

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References

  1. E.ACERBI-N.FUSCO, Semicontinuity problems in the calculus of variations, Arch. Rat. Mech. Analysis, to appear.

    Google Scholar 

  2. G. AUBERT-R. TAHRAOUI, Théorèmes d’existence en calcul des variations, C. R. Acad. Sc. Paris, 285 (1977), 355–356.

    MathSciNet  MATH  Google Scholar 

  3. G. AUBERT-R. TAHRAOUI, Théorèmes d’existence pour des problèmes du calcul des variations..., J. Differential Equations, 33 (1979), 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  4. J.M. BALL, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Analysis, 63 (1977), 337–403.

    Article  MathSciNet  MATH  Google Scholar 

  5. L.D. BERKOWITZ, Lower semicontinuity of integral functionals, Trans. Am. Math. Soc., 192 (1974), 51–57.

    Article  MathSciNet  Google Scholar 

  6. L. CESARI, Lower semicontinuity and lower closure theorems without seminormality condition, Annali Mat. Pura Appl., 98 (1974), 381–397.

    Article  MathSciNet  MATH  Google Scholar 

  7. E. DE GIORGI, Teoremi di semicontinuità nel calcolo delle variazioni, Istit. Naz. Alta Mat., Roma (1968–1969).

    Google Scholar 

  8. I.EKELAND-R.TEMAM, Analyse convexe et problèmes variationnels, Dunod Gauthier-Villars, 1974.

    Google Scholar 

  9. H.FEDERER, Geometric measure theory, Die Grundl. Math. Wiss. 153, Springer-Verlag, 1969.

    Google Scholar 

  10. P. HARTMAN-G. STAMPACCHIA, On some non-linear elliptic differential-functional equations, Acta Math., 115 (1966), 271–310.

    Article  MathSciNet  MATH  Google Scholar 

  11. A.D. IOFFE, On lower semicontinuity of integral functional I, SIAM J. Cont. Optimization, 15 (1977), 521–538.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. KLOTZLER, On the existence of optimal processes, Banach Center Publications, Volume 1, Warszawa 1976, 125–130.

    Google Scholar 

  13. P. MARCELLINI, Alcune osservazioni sull’esistenza del minimo di integrali del calcolo delle variazioni senza ipotesi di convessità, Rendiconti Mat., 13 (1980), 271–281.

    MathSciNet  MATH  Google Scholar 

  14. P. MARCELLINI-C. SBORDONE, Semicontinuity problems in the calculus of variations, Nonlinear Analysis, 4 (1980), 241–257.

    Article  MathSciNet  MATH  Google Scholar 

  15. P.MARCELLINI-C.SBORDONE, On the existence of minima of multiple integrals of the calculus of variations, J. Math. Pures Appl., to appear.

    Google Scholar 

  16. E.MASCOLO-R.SCHIANCHI, Existence theorems for non convex problems, to appear.

    Google Scholar 

  17. C.B. MORREY, Quasiconvexity and the lower semicontinuity of multiple integrals, Pacific J. Math., 2 (1952), 25–53.

    Article  MathSciNet  MATH  Google Scholar 

  18. C.B.MORREY, Multiple integrals in the calculus of variations, Die Grundl. Math. Wiss. 130, Springer-Verlag, 1966.

    Google Scholar 

  19. 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), 109–125.

    Google Scholar 

  20. C. OLECH, A characterization of L1-weak lower semicontinuity of integral functional, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys., 25 (1977), 135–142.

    MathSciNet  MATH  Google Scholar 

  21. P.OPPEZZI, Convessità della integranda in un funzionale del calcolo delle variazioni, Boll. Un. Mat. Ital., to appear.

    Google Scholar 

  22. J. SERRIN, On the definition and properties of certain variational integrals, Trans. Am. Math. Soc., 101 (1961), 139–167.

    Article  MathSciNet  MATH  Google Scholar 

  23. L.TONELLI, Fondamenti di calcolo delle variazioni, Volume I, Zanichelli, 1921.

    Google Scholar 

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Authors

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Jaurés P. Cecconi Tullio Zolezzi

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© 1983 Springer-Verlag

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Marcellini, P. (1983). A relation between existence of minima for non convex integrals and uniqueness for non strictly convex integrals of the calculus of variations. In: Cecconi, J.P., Zolezzi, T. (eds) Mathematical Theories of Optimization. Lecture Notes in Mathematics, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066256

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  • DOI: https://doi.org/10.1007/BFb0066256

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  • Print ISBN: 978-3-540-11999-9

  • Online ISBN: 978-3-540-39473-0

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