Existence of ${C}^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 40 (2007) no. 3, p. 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},
publisher = {Elsevier},
volume = {Ser. 4, 40},
number = {3},
year = {2007},
pages = {445-452},
doi = {10.1016/j.ansens.2007.01.004},
zbl = {1133.35027},
language = {en},
url = {http://www.numdam.org/item/ASENS_2007_4_40_3_445_0}
}

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, Serie 4, Volume 40 (2007) no. 3, pp. 445-452. doi : 10.1016/j.ansens.2007.01.004. http://www.numdam.org/item/ASENS_2007_4_40_3_445_0/

[1] Bernard P., The dynamics of pseudographs in convex Hamiltonian systems, J. Am. Math. Soc., in press.

[2] Cannarsa P., Sinestrari C., Semiconcave Functions, Hamilton-Jacobi Equations and Optimal Control, Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, 2004. | Zbl 1095.49003

[3] Contreras G., Iturriaga R., Paternain G.P., Paternain M., Lagrangian graphs, minimizing measures and Mañé's critical values, Geom. Funct. Anal. 8 (5) (1998) 788-809. | MR 1650090 | Zbl 0920.58015

[4] Fathi A., Weak KAM Theorem in Lagrangian Dynamics, book in press.

[5] Fathi A., Siconolfi A., Existence of ${C}^{1}$ critical sub-solutions of the Hamilton-Jacobi equation, Invent. Math. 155 (2) (2004) 363-388. | Zbl 1061.58008

[6] Fathi A., Siconolfi A., PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians, Calc. Var. Partial Differential Equations 22 (2005) 185-228. | Zbl 1065.35092

[7] Lasry J.M., Lions J.L., A remark on regularization in Hilbert spaces, Israel J. Math. 55 (3) (1986) 257-266. | MR 876394 | Zbl 0631.49018

[8] Massart D., Sub-solutions of time-periodic Hamilton-Jacobi equations, Ergodic Theory Dynam. Systems, in press. | Zbl 1121.37049