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Viscosity solution methods and the discrete Aubry-Mather problem
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.
dual problem turns out to be a
discrete analog of the Hamilton-Jacobi equations.
We present some applications to discretizations of Lagrangian