no. 3
Existence of C 1,1 critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 3, pp. 445-452. 
@article{ASENS_2007_4_40_3_445_0,
     author = {Bernard, Patrick},
     title = {Existence of ${C}^{1,1}$ critical sub-solutions of the {Hamilton-Jacobi} equation on compact manifolds},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {445--452},
     publisher = {Elsevier},
     volume = {Ser. 4, 40},
     number = {3},
     year = {2007},
     doi = {10.1016/j.ansens.2007.01.004},
     zbl = {1133.35027},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2007.01.004/}
}
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Bernard, Patrick. Existence of ${C}^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 3, pp. 445-452. doi : 10.1016/j.ansens.2007.01.004. http://archive.numdam.org/articles/10.1016/j.ansens.2007.01.004/

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