M. Arnaud, Le ??closing lemma?? en topologie $C^1$, Mémoires de la Société mathématique de France, vol.1, 1998.
DOI : 10.24033/msmf.387

P. Bernard, Existence of C1,1C1,1 critical sub-solutions of the Hamilton???Jacobi equation on compact manifolds, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.40, issue.3, pp.445-452, 2007.
DOI : 10.1016/j.ansens.2007.01.004

URL : https://hal.archives-ouvertes.fr/hal-00014965

P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations, and optimal control, Progress in Nonlinear Differential Equations and their Applications, 2004.

A. Fathi, Regularity of C$^1$ solutions of the Hamilton-Jacobi equation, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.12, issue.4, pp.479-516, 2003.
DOI : 10.5802/afst.1059

A. Fathi, Weak KAM Theorem and Lagrangian Dynamics

A. Fathi and E. Maderna, Weak kam theorem on non compact manifolds, Nonlinear Differential Equations and Applications NoDEA, vol.14, issue.1-2, pp.1-27, 2007.
DOI : 10.1007/s00030-007-2047-6

URL : http://arxiv.org/abs/1502.06247

A. Fathi and A. Siconolfi, Existence of C 1 critical subsolutions of the Hamilton-Jacobi equation, Inventiones Mathematicae, vol.155, issue.2, pp.363-388, 2004.
DOI : 10.1007/s00222-003-0323-6

A. Figalli and L. Rifford, Closing Aubry sets I, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00935965

Y. Li and L. Nirenberg, The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations, Communications on Pure and Applied Mathematics, vol.15, issue.1, pp.85-146, 2005.
DOI : 10.1002/cpa.20051

J. Mai, A simpler proof of C 1 closing lemma, Sci. Sinica Ser. A, vol.29, issue.10, pp.1020-1031, 1986.

R. Mañé, Generic properties and problems of minimizing measures of Lagrangian systems, Nonlinearity, vol.9, issue.2, pp.273-310, 1996.
DOI : 10.1088/0951-7715/9/2/002

L. Rifford, On Viscosity Solutions of Certain Hamilton???Jacobi Equations: Regularity Results and Generalized Sard's Theorems, Communications in Partial Differential Equations, vol.149, issue.3, pp.517-559, 2008.
DOI : 10.1016/j.anihpc.2005.05.002

L. Rifford, Nonholonomic Variations: An introduction to sub-Riemannian geometry