Existence of lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case

A. Cellina; A. Ferriero

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 6, page 911-919
  • ISSN: 0294-1449

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Cellina, A., and Ferriero, A.. "Existence of lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case." Annales de l'I.H.P. Analyse non linéaire 20.6 (2003): 911-919. <http://eudml.org/doc/78604>.

@article{Cellina2003,
author = {Cellina, A., Ferriero, A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {calculus of variations; existence and Lipschitzianity of solutions; functional integral},
language = {eng},
number = {6},
pages = {911-919},
publisher = {Elsevier},
title = {Existence of lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case},
url = {http://eudml.org/doc/78604},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Cellina, A.
AU - Ferriero, A.
TI - Existence of lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 6
SP - 911
EP - 919
LA - eng
KW - calculus of variations; existence and Lipschitzianity of solutions; functional integral
UR - http://eudml.org/doc/78604
ER -

References

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  1. [1] A. Cellina, Reparametrizations and the non-occurrence of the Lavrentiev phenomenon in the autonomous case of the calculus of variations, Preprint, 2001. 
  2. [2] A. Cellina, The classical problem of the calculus of variations in the autonomous case: Relaxation and Lipschitzianity of solutions, Trans. Amer. Math. Soc., submitted for publication. Zbl1064.49027MR2020039
  3. [3] Cellina A., Treu G., Zagatti S., On the minimum problem for a class of non-coercive functionals, J. Differential Equations127 (1996) 225-262. Zbl0856.49010MR1387265
  4. [4] Cesari L., Optimization, Theory and Applications, Springer-Verlag, New York, 1983. Zbl0506.49001MR688142
  5. [5] Clarke F.H., Vinter R.B., Regularity properties of solutions to the basic problem in the calculus of variations, Trans. Amer. Math. Soc.289 (1985) 73-98. Zbl0563.49009MR779053
  6. [6] Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. Zbl0322.90046MR463994
  7. [7] Serrin J., Varberg D.E., A general chain rule for derivatives and the change of variable formula for the Lebesgue integral, Amer. Math. Monthly76 (1969) 514-520. Zbl0175.34401MR247011

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