Convergence of the solutions of discounted Hamilton--Jacobi systems
Analysis of PDEs
2017-03-31 v1
Abstract
We consider a weakly coupled system of discounted Hamilton--Jacobi equations set on a closed Riemannian manifold. We prove that the corresponding solutions converge to a specific solution of the limit system as the discount factor goes to zero. The analysis is based on a generalization of the theory of Mather minimizing measures for Hamilton--Jacobi systems and on suitable random representation formulae for the discounted solutions.
Keywords
Cite
@article{arxiv.1702.07530,
title = {Convergence of the solutions of discounted Hamilton--Jacobi systems},
author = {Andrea Davini and Maxime Zavidovique},
journal= {arXiv preprint arXiv:1702.07530},
year = {2017}
}