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Mather problem for stationary Lagrangians

Bibliography:

D. Gomes, E. Oliveira, Mather problem for stationary Lagrangians,

S. Paulo Math. Journal,  (2012), no. 2, 301–334

Authors:

D. Gomes, E. Oliveira

Keywords:

Aubry-Mather theory, Stationary Lagrangians, Stationary Viscosity Solutions

Year:

2012

Abstract:

In this paper we discuss the Mather problem for stationary Lagrangians, that is Lagrangians L : Rn × Rn × Ω → R, where Ω is a compact metric space on which Rn acts through an action which leaves L invariant. This setting allow us to generalize the standard Mather problem for quasi-periodic and almost-periodic Lagrangians. Our main result is the existence of stationary Mather measures invariant under the Euler-Lagrange flow which are supported in a graph. We also obtain several estimates for viscosity solutions of Hamilton-Jacobi equations for the discounted cost infinite horizon problem.

ISSN:

2012