Viscosity solution methods and the discrete Aubry-Mather problem

Pages: 103 - 116, Volume 13, Issue 1, June 2005

doi:10.3934/dcds.2005.13.103       Abstract        Full Text (200.6K)       Related Articles

Diogo A. Gomes - Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal (email)

Abstract: 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, 70H20.

Received: April 2004;      Revised: November 2004;      Published: March 2005.