Showing papers by "Hitoshi Ishii published in 1996"
TL;DR: In this article, the first-order Hamilton-Jacobi-Bellman equation associated with the state constraint problem for optimal control is studied, and a new and appropriate boundary condition for the PDE is proposed.
Abstract: The first-order Hamilton--Jacobi--Bellman equation associated with the state constraint problem for optimal control is studied. Instead of the boundary condition which Soner introduced, a new and appropriate boundary condition for the PDE is proposed. The uniqueness and Lipschitz continuity of viscosity solutions for the boundary value problem are obtained.
75 citations
Journal Article•
TL;DR: In this paper, Ohnuma-Sato et al. established comparison theorems for solutions of degenerate parabolic partial differential equations with discontinuities (or singularities).
Abstract: We establish comparison theorems for solutions of degenerate parabolic partial differential equations with discontinuities (or singularities). The results are used to define the generalized evolutions of sets generated by geometric partial differential equations with discontinuities. These results generalize recent results obtained by Ohnuma-Sato ([13]) and Gurtin-Soner-Souganidis ([11]).
16 citations