# 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} }

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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