# Viscosity solution methods and the discrete Aubry-Mather problem

@article{Gomes2005ViscositySM,
title={Viscosity solution methods and the discrete Aubry-Mather problem},
author={Diogo A. Gomes},
journal={Discrete and Continuous Dynamical Systems},
year={2005},
volume={13},
pages={103-116}
}
• D. Gomes
• Published 1 March 2005
• Mathematics
• Discrete and Continuous Dynamical Systems
In this paper we study a discrete multi-dimensional version of Aubry-Mather theory using mostly tools from the theory of viscosity solutions. We set this problem as an infinite dimensional linear programming problem. The dual problem turns out to be a discrete analog of the Hamilton-Jacobi equations. We present some applications to discretizations of Lagrangian systems.

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