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

Diogo A. Gomes, Hiroyoshi Mitake, Hung V. Tran

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)345-364
Number of pages20
JournalJournal of the Mathematical Society of Japan
Volume70
Issue number1
DOIs
StatePublished - Jan 1 2018

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