Viscosity solution methods and the discrete Aubry-Mather problem

Diogo A. Gomes

doi:10.3934/dcds.2005.13.103

Viscosity solution methods and the discrete Aubry-Mather problem

Diogo A. Gomes^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

30 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 language	English (US)
Pages (from-to)	103-116
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems
Volume	13
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2005.13.103
State	Published - Jun 2005
Externally published	Yes

Keywords

Aubry-Mather theory
Discrete Hamiltonian systems
Viscosity Solutions

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2005.13.103

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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.",

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AB - 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.

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Viscosity solution methods and the discrete Aubry-Mather problem

Abstract

Keywords

ASJC Scopus subject areas

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