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arXiv · 1906.07979

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

Hitoshi Ishii·Liang Jin
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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.

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Hitoshi Ishii, Liang Jin. 2020-04-19. The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: Nonlinear coupling. https://arxiv.org/abs/1906.07979

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