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Article Contents

# 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. The dual problem turns out to be a discrete analog of the Hamilton-Jacobi equations. We present some applications to discretizations of Lagrangian systems.
Mathematics Subject Classification: 49L25, 37J40, 37J50, 70H20.

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