The vanishing discount problem for Hamilton–Jacobi equations in the Euclidean space

DOI10.1080/03605302.2019.1710845zbMath1442.35032arXiv1908.00869OpenAlexW3003570566MaRDI QIDQ3296352

Hitoshi Ishii, Antonio Siconolfi

Publication date: 7 July 2020

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.00869

zbMATH Keywords

ergodic problembounded generalized Lagrangians

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Hamilton-Jacobi equations (35F21)

Related Items (12)

Asymptotic analysis for Hamilton-Jacobi-Bellman equations on Euclidean space ⋮ The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. I: Linear coupling ⋮ Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint ⋮ Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function ⋮ A Selection Principle for Weak KAM Solutions via Freidlin–Wentzell Large Deviation Principle of Invariant Measures ⋮ Hamilton Dynamics in Chemical Reactions: the Maupertuis Principle, Transition Paths and Energy Landscape ⋮ The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. II: Nonlinear coupling ⋮ On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case ⋮ 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 ⋮ An eikonal equation with vanishing Lagrangian arising in global optimization ⋮ Convergence of solutions for some degenerate discounted Hamilton-Jacobi equations

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