## 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 language | English (US) |
---|---|

Pages (from-to) | 345-364 |

Number of pages | 20 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 70 |

Issue number | 1 |

DOIs | |

State | Published - 2018 |

## Keywords

- Discounted approximation
- Ergodic problems
- Nonlinear adjoint methods
- nonconvex Hamilton–Jacobi equations

## ASJC Scopus subject areas

- General Mathematics