Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds

Patrick Bernard (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We prove the existence of a critical subsolution of the Hamilton-Jacobi equation which is differentiable with Lipschitz differential, improving a previous result of Fathi and Siconolfi. This text is a consolidated version with a minor mistake corrected from the published version.

Mots clés: Weak KAM theory; viscosity solutions; subsolutions; Hamilton-Jacobi equation

Domaines: Systèmes dynamiques [math.DS]; Equations aux dérivées partielles [math.AP]

Patrick Bernard. Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds. Annales Scientifiques de l'École Normale Supérieure, 2007, 40 (3), pp.445-452. ⟨hal-00014965v4⟩