Vanishing discount and viscosity selection problems for mechanical Hamilton--Jacobi equations
Year: 2026
Type: preprint
Abstract: We study simultaneous vanishing discount and viscosity limits for mechanical Hamilton--Jacobi equations on the $n$-dimensional torus. In the critical regime, we explicitly identify the selected limit in terms of the critical Mañé potential and the quadratic behavior of the potential near its wells. We also obtain quantitative and sharp convergence estimates in the subcritical regime. In the supercritical regime, we prove convergence when the local harmonic ground-state energy of the potential has a unique minimizer among the wells. Finally, we establish a concentration phenomenon of the associated Gibbs measures.
Source: arXiv (Cornell University)
Authors: Mitake, Hiroyoshi, Ni, Panrui, Tran, Hung V.
Institution: Waseda University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Quantitative homogenization theory of fully nonlinear partial differential equations, Mathematical analysis on interface motions allowing collision, rupture and coalasce, Viscosity Solutions: Beyond the Wellposedness Theory, Quantitative homogenization theory for Hamilton–Jacobi equations, Research on the theory and applications of viscosity solutions based on asymptotic and boundary value problems, Development of Discrete Mean Field Game Theory
OpenAlex ID: W7214020940