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

DOI10.1016/j.matpur.2019.04.005zbMath1428.35088arXiv1801.06008OpenAlexW2964134014WikidataQ124843212 ScholiaQ124843212MaRDI QIDQ2314031

Bruno Ziliotto

Publication date: 19 July 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.06008

zbMATH Keywords

zero-sum games

Mathematics Subject Classification ID

2-person games (91A05) Asymptotic behavior of solutions to PDEs (35B40) Stochastic games, stochastic differential games (91A15) Dynamic games (91A25) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21)

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An example of failure of stochastic homogenization for viscous Hamilton-Jacobi equations without convexity ⋮ Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem ⋮ Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function ⋮ Remarks on the vanishing discount problem for infinite systems of Hamilton-Jacobi-Bellman equations ⋮ The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. II: Nonlinear coupling ⋮ Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: the central role of Mather measures ⋮ The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: a counterexample to the full convergence ⋮ Fixed points of contractions approximating 1-Lipschitz maps ⋮ Unique ergodicity of deterministic zero-sum differential games ⋮ Convergence of solutions for some degenerate discounted Hamilton-Jacobi equations

Cites Work

• Zero-sum repeated games: counterexamples to the existence of the asymptotic value and the conjecture \({\max}{\min}=\lim v_{n}\)
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• Stochastic Homogenization of Nonconvex Hamilton‐Jacobi Equations: A Counterexample
• A deterministic‐control‐based approach motion by curvature