Convergence of the solutions of discounted Hamilton–Jacobi systems-Reference-Cited by-同舟云学术

Convergence of the solutions of discounted Hamilton–Jacobi systems

Published:2019-02-15 Issue:2 Volume:14 Page:193-206
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Davini Andrea¹^ORCID,Zavidovique Maxime²

Affiliation:

1. Dipartimento di Matematica , Sapienza Università di Roma , Piazzale le Aldo Moro 2, 00185 Roma , Italy

2. IMJ-PRG (projet Analyse Algébrique) , UPMC , 4, place Jussieu, Case 247, 75252 Paris Cedex 5 , France

Abstract

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 0. 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.

Funder

Agence Nationale de la Recherche

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2018-0037/pdf

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