The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
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AbstractHere, 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.
CitationGOMES DA, MITAKE H, TRAN HV (2018) The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases. Journal of the Mathematical Society of Japan 70: 345–364. Available: http://dx.doi.org/10.2969/jmsj/07017534.