Mather problem and viscosity solutions in the stationary setting

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In this paper we discuss the Mather problem for stationary Lagrangians, that is Lagrangians $L:\Rr^n\times \Rr^n\times Ω\to \Rr$, where $Ω$ is a compact metric space on which $\Rr^n$ 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.

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Analysis of PDEs, Dynamical Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/222712

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0903.1594
 http://arxiv.org/abs/0903.1594

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arXiv