Geodesic
Necessary conditions for an extremum in the calculus of variations with nonsmooth phase variables
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 922-930.

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Necessary conditions for an extremum in a general isoperimetric problem not involving partial derivatives with respect to phase variables are obtained. 
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V. Jankovic. Necessary conditions for an extremum in the calculus of variations with nonsmooth phase variables. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 922-930. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a11/

[1] Jankovič V., “Necessary conditions in a problem of calculus of variations”, Publ. Inst. Math. (Beograd), 45 (59) (1989), 143–151 | MR | Zbl

[2] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Nauka, M., 1979