The vanishing discount problem for nonlocal Hamilton-Jacobi equations

2025/04/16 by Davini, Andrea, Ishii, Hitoshi · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2504.11789

Abstract

We establish a convergence result for the vanishing discount problem in the context of nonlocal HJ equations. We consider a fairly general class of discounted first-order and convex HJ equations which incorporate an integro-differential operator posed on the d-dimensional torus, and we show that the solutions converge to a specific critical solution as the discount factor tends to zero. Our approach relies on duality techniques for nonlocal convex HJ equations, building upon Hahn-Banach separation theorems to develop a generalized notion of Mather measure. The results are applied to a specific class of convex and superlinear Hamiltonians.

Cited by

• On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount
• Vanishing discount limits for first-order fully nonlinear Hamilton-Jacobi equations on noncompact domains

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