Aubry-Mather measures in the non convex setting

Abstract

The adjoint method introduced in [Eva] and [Tra] is used, to construct analogs to the Aubry-Mather measures for non convex Hamiltonians. More precisely, a general construction of probability measures, that in the convex setting agree with Mather measures, is provided. These measures may fail to be invariant under the Hamiltonian flow and a dissipation arises, which is described by a positive semidefinite matrix of Borel measures. However, in the important case of uniformly quasiconvex Hamiltonians the dissipation vanishes, and as a consequence the invariance is guaranteed.

final version

References in corpus (1)

• Adjoint methods for static Hamilton-Jacobi equations

Cited by in corpus (3)

• On the regularity of stochastic effective Hamiltonian
• Vanishing discount limits for first-order fully nonlinear Hamilton-Jacobi equations on noncompact domains
• Mather measures for space-time periodical nonconvex hamiltonians