Aubry-Mather measures in the non convex setting
Analysis of PDEs
2012-01-04 v2
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.
Cite
@article{arxiv.1005.1317,
title = {Aubry-Mather measures in the non convex setting},
author = {Filippo Cagnetti and Diogo Gomes and Hung Tran},
journal= {arXiv preprint arXiv:1005.1317},
year = {2012}
}
Comments
final version