Convergence of solutions for some degenerate discounted Hamilton–Jacobi equations

where $α$ is a nonnegative function, $λ$ a positive constant, $c$ a constant and $H$ a convex coercive Hamiltonian. Under suitable conditions on $α$ we prove that the functions $u_{λ}$ converge as $λ \to 0$ to a function $u_{0}$ that is a solution of the critical equation $H (x, D_{x} u_{0}) = c$ .

Keywords

discounted Hamilton–Jacobi equations, viscosity solutions, weak KAM theory, Mather measures

Mathematical Subject Classification

Primary: 35D40, 35F21, 49L25

Milestones

Received: 10 June 2020

Accepted: 18 January 2021

Published: 29 September 2022

Authors

Maxime Zavidovique
Sorbonne Université and Université de Paris, CNRS, IMJ-PRG Paris France

Vol. 15, No. 5, 2022

Maxime Zavidovique

Abstract

Keywords

Mathematical Subject Classification

Milestones

Authors