The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 1: linear coupling
Analysis of PDEs
2020-06-25 v2
Abstract
We establish a convergence theorem for the vanishing discount problem for a weakly coupled system of Hamilton-Jacobi equations. The crucial step is the introduction of Mather measures and their relatives for the system, which we call respectively viscosity Mather and Green-Poisson measures. This is done by the convex duality and the duality between the space of continuous functions on a compact set and the space of Borel measures on it. This is part 1 of our study of the vanishing discount problem for systems, which focuses on the linear coupling, while part 2 will be concerned with nonlinear coupling.
Keywords
Cite
@article{arxiv.1903.00244,
title = {The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 1: linear coupling},
author = {Hitoshi Ishii},
journal= {arXiv preprint arXiv:1903.00244},
year = {2020}
}
Comments
26 pages. arXiv admin note: text overlap with arXiv:1906.07979