H
Hitoshi Ishii
Researcher at Tsuda College
Publications - 135
Citations - 11150
Hitoshi Ishii is an academic researcher from Tsuda College. The author has contributed to research in topics: Hamilton–Jacobi equation & Nonlinear system. The author has an hindex of 37, co-authored 133 publications receiving 10376 citations. Previous affiliations of Hitoshi Ishii include Hokkaido University & Brown University.
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User’s guide to viscosity solutions of second order partial differential equations
TL;DR: The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorem, and continuous dependence may now be proved by very efficient and striking arguments as discussed by the authors.
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Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
Hitoshi Ishii,Pierre-Louis Lions +1 more
TL;DR: In this paper, Jensen and Ishii investigated comparison and existence results for viscosity solutions of fully nonlinear, second-order, elliptic, possibly degenerate equations, and applied these methods and results to quasilinear Monge-Ampere equations.
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Perron’s method for Hamilton-Jacobi equations
TL;DR: On considere l'existence des solutions d'equations aux derivees partielles non lineaires scalaires d'ordre 1: F(x, u, Du) = 0 dans Ω, ou Ω est un sous-ensemble ouvert de R N, F: Ω×R×R N →R →R est continue, u:Ω→R est l'inconnue as mentioned in this paper.
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On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's
TL;DR: In this paper, a comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations are presented. But they do not consider the existence of continuous solutions.
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On lipschitz continuity of the solution mapping to the skorokhod problem, with applications
Paul Dupuis,Hitoshi Ishii +1 more
TL;DR: In this article, the authors focus on the case where the set is a convex polyhedron and where the directions along which the constraint mechanism is applied arc possibly oblique and multivalued at corner points.