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

Abstract

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.

References in corpus (2)

• The dynamics of pseudographs in convex Hamiltonian systems
• Smooth critical sub-solutions of the Hamilton-Jacobi equation

Cited by in corpus (4)

• Homoclinic orbits and critical points of barrier functions
• On the number of Mather measures of Lagrangian systems
• Weak KAM for commuting Hamiltonians
• Characterization of minimizable Lagrangian action functionals and a dual Mather theorem