TY - JOUR

T1 - The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases

AU - Gomes, Diogo A.

AU - Mitake, Hiroyoshi

AU - Tran, Hung V.

N1 - KAUST Repository Item: Exported on 2020-04-23

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/627149

UR - https://projecteuclid.org/euclid.jmsj/1516957230#info

UR - http://www.scopus.com/inward/record.url?scp=85041907772&partnerID=8YFLogxK

U2 - 10.2969/jmsj/07017534

DO - 10.2969/jmsj/07017534

M3 - Article

AN - SCOPUS:85041907772

SN - 0025-5645

VL - 70

SP - 345

EP - 364

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 1

ER -