Convergence of the solutions of the discounted Hamilton-Jacobi equation: a counterexample

Abstract

This paper provides a counterexample about the asymptotic behavior of the solutions of a discounted Hamilton-Jacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1-dimensional continuous and coercive Hamiltonian.

References in corpus (1)

• Convergence of the solutions of the discounted equation: the discrete case

Cited by in corpus (3)

• Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function
• A note on existence and asymptotic behavior of Lagrangian equilibria for first-order optimal-exit mean field games
• Remarks on the vanishing discount problem for infinite systems of Hamilton-Jacobi-Bellman equations