Viscosity solution methods and the discrete Aubry-Mather problem

Diogo Gomes*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

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 but to be a discrete analog of the Hamilton-Jacobi equations. We present some applications to discretizations of Lagrangian systems.

Original languageEnglish (US)
Pages (from-to)103-116
Number of pages14
JournalDiscrete and Continuous Dynamical Systems
Volume13
Issue number1
DOIs
StatePublished - Jan 1 2005

Keywords

  • Aubry-Mather theory
  • Discrete Hamiltonian systems
  • Viscosity Solutions

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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