Smooth critical sub-solutions of the Hamilton-Jacobi equation

Patrick Bernard (1, 2, 3)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 PSL - Université Paris sciences et lettres

We establish the existence of smooth critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union of finitely many hyperbolic periodic orbits.

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

Patrick Bernard. Smooth critical sub-solutions of the Hamilton-Jacobi equation. Mathematical Research Letters, 2007, 14 (3), pp.503 - 511. ⟨10.4310/MRL.2007.v14.n3.a14⟩. ⟨hal-00014966v2⟩