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January, 2018 The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases
Diogo A. GOMES, Hiroyoshi MITAKE, Hung V. TRAN
J. Math. Soc. Japan 70(1): 345-364 (January, 2018). DOI: 10.2969/jmsj/07017534


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. "The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases." J. Math. Soc. Japan 70 (1) 345 - 364, January, 2018.


Published: January, 2018
First available in Project Euclid: 26 January 2018

zbMATH: 06859855
MathSciNet: MR3750279
Digital Object Identifier: 10.2969/jmsj/07017534

Primary: 35B40
Secondary: 37J50 , 49L25

Keywords: discounted approximation , ergodic problems , nonconvex Hamilton–Jacobi equations , nonlinear adjoint methods

Rights: Copyright © 2018 Mathematical Society of Japan


Vol.70 • No. 1 • January, 2018
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