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 -