no. 6
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, Tome 20 (2003) no. 6, pp. 911-919. 
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     author = {Cellina, A. and Ferriero, A.},
     title = {Existence of lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {911--919},
     publisher = {Elsevier},
     volume = {20},
     number = {6},
     year = {2003},
     doi = {10.1016/S0294-1449(03)00010-6},
     mrnumber = {2008683},
     zbl = {1030.49039},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S0294-1449(03)00010-6/}
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Cellina, A.; 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, Tome 20 (2003) no. 6, pp. 911-919. doi : 10.1016/S0294-1449(03)00010-6. http://archive.numdam.org/articles/10.1016/S0294-1449(03)00010-6/

[1] A. Cellina, Reparametrizations and the non-occurrence of the Lavrentiev phenomenon in the autonomous case of the calculus of variations, Preprint, 2001.

[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. | MR | Zbl

[3] Cellina A., Treu G., Zagatti S., On the minimum problem for a class of non-coercive functionals, J. Differential Equations 127 (1996) 225-262. | MR | Zbl

[4] Cesari L., Optimization, Theory and Applications, Springer-Verlag, New York, 1983. | MR | Zbl

[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. | MR | Zbl

[6] Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. | MR | Zbl

[7] Serrin J., Varberg D.E., A general chain rule for derivatives and the change of variable formula for the Lebesgue integral, Amer. Math. Monthly 76 (1969) 514-520. | MR | Zbl

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