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.

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Cited by in corpus (6)

• Convergence of solutions for some degenerate discounted Hamilton--Jacobi equations
• Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function
• The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: Nonlinear coupling
• A note on existence and asymptotic behavior of Lagrangian equilibria for first-order optimal-exit mean field games
• An example in the vanishing discount problem for monotone systems of Hamilton-Jacobi equations
• Remarks on the vanishing discount problem for infinite systems of Hamilton-Jacobi-Bellman equations