Calculus of Variations and Geometric Measure Theory

A. Davini - M. Zavidovique

Convergence of the solutions of discounted Hamilton--Jacobi systems

created by davini on 12 Jul 2023


Published Paper

Inserted: 12 jul 2023
Last Updated: 12 jul 2023

Journal: Adv. Calc. Var.
Volume: 14
Number: 2
Pages: 193–206
Year: 2021

ArXiv: 1702.07530 PDF


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.