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April  2005, 13(1): 103-116. doi: 10.3934/dcds.2005.13.103

Viscosity solution methods and the discrete Aubry-Mather problem

Diogo A. Gomes 1,

1. 

Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Received  April 2004 Revised  November 2004 Published  March 2005

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.
Keywords: Viscosity Solutions, Aubry-Mather theory, discrete Hamiltonian systems..
Mathematics Subject Classification: 49L25, 37J40, 37J50, 70H2.
Citation: Diogo A. Gomes. Viscosity solution methods and the discrete Aubry-Mather problem. Discrete & Continuous Dynamical Systems, 2005, 13 (1) : 103-116. doi: 10.3934/dcds.2005.13.103
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