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arXiv · 1605.07532

The Selection problem for discounted Hamilton-Jacobi equations: some non-convex cases

Diogo A. Gomes·Hiroyoshi Mitake·Hung V. Tran
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Abstract

Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton-Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton-Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton-Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.

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Diogo A. Gomes, Hiroyoshi Mitake, Hung V. Tran. 2016-05-24. The Selection problem for discounted Hamilton-Jacobi equations: some non-convex cases. https://arxiv.org/abs/1605.07532

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