English

The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: Nonlinear coupling

Analysis of PDEs 2020-04-21 v2

Abstract

We study the vanishing discount problem for a nonlinear monotone system of Hamilton-Jacobi equations. This continues the first author's investigation on the vanishing discount problem for a monotone system of Hamilton-Jacobi equations. As in Part 1, we introduce by the convex duality Mather measures and their analogues for the system, which we call respectively Mather and Green-Poisson measures, and prove a convergence theorem for the vanishing discount problem. Moreover, we establish an existence result for the ergodic problem.

Keywords

Cite

@article{arxiv.1906.07979,
  title  = {The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: Nonlinear coupling},
  author = {Hitoshi Ishii and Liang Jin},
  journal= {arXiv preprint arXiv:1906.07979},
  year   = {2020}
}

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36 pages