Viscosity solution methods and the discrete Aubry-Mather problem
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
Received: April 2004; Revised: November 2004; Published: March 2005.
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