2013 - Fellow of the American Mathematical Society
His primary areas of study are Mathematical analysis, Partial differential equation, Uniqueness, Hamilton–Jacobi equation and Viscosity solution. His work on Boundary value problem as part of general Mathematical analysis study is frequently linked to Viscosity, therefore connecting diverse disciplines of science. His study in Partial differential equation is interdisciplinary in nature, drawing from both Elliptic curve and Existence theorem.
His Uniqueness research is multidisciplinary, relying on both Exponential stability, Hilbert space and Asymptotic analysis. His biological study spans a wide range of topics, including Open set, Pure mathematics, Uniqueness theorem for Poisson's equation and Algebra. He works mostly in the field of Viscosity solution, limiting it down to concerns involving Differential equation and, occasionally, Mathematical proof.
The scientist’s investigation covers issues in Mathematical analysis, Hamilton–Jacobi equation, Partial differential equation, Applied mathematics and Boundary value problem. His study in the field of Viscosity solution, Uniqueness, Parabolic partial differential equation and Initial value problem also crosses realms of Degenerate energy levels. His studies deal with areas such as Bellman equation, Euclidean space and Differential equation as well as Viscosity solution.
His Hamilton–Jacobi equation research incorporates elements of Mathematical physics, Pure mathematics and Regular polygon. His work is dedicated to discovering how Partial differential equation, Elliptic curve are connected with Elliptic partial differential equation and other disciplines. Hitoshi Ishii combines subjects such as Bounded function, Type, Domain and Asymptotic analysis with his study of Boundary value problem.
His scientific interests lie mostly in Degenerate energy levels, Mathematical analysis, Hamilton–Jacobi equation, Applied mathematics and Dirichlet problem. Variable, Boundary value problem and Viscosity solution are the core of his Mathematical analysis study. His work deals with themes such as Orthant, Type and Hamilton–Jacobi–Bellman equation, Bellman equation, which intersect with Viscosity solution.
His Hamilton–Jacobi equation study combines topics in areas such as Ergodic theory and Regular polygon. Hitoshi Ishii combines Applied mathematics and Viscosity in his studies. His work focuses on many connections between Partial differential equation and other disciplines, such as Series, that overlap with his field of interest in Parabolic partial differential equation, Representation and Neumann boundary condition.
Hamilton–Jacobi equation, Degenerate energy levels, Mathematical analysis, Pure mathematics and Applied mathematics are his primary areas of study. In his papers, he integrates diverse fields, such as Degenerate energy levels, Partial differential equation, Elliptic operator, Dirichlet problem and Convexity. His Partial differential equation study incorporates themes from Neumann boundary condition, Series, Viscosity and Torus.
Ergodic theory and Boundary value problem are among the areas of Mathematical analysis where Hitoshi Ishii concentrates his study. His research investigates the connection with Pure mathematics and areas like Eigenvalues and eigenvectors which intersect with concerns in Order, Domain, Convex function, Existence theorem and Laplace operator. In his works, Hitoshi Ishii performs multidisciplinary study on Applied mathematics and Viscosity.
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User’s guide to viscosity solutions of second order partial differential equations
Michael G. Crandall;Hitoshi Ishii;Pierre Louis Lions.
Bulletin of the American Mathematical Society (1992)
Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
H Ishii;P.L Lions.
Journal of Differential Equations (1990)
Perron’s method for Hamilton-Jacobi equations
Duke Mathematical Journal (1987)
On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's
Communications on Pure and Applied Mathematics (1989)
On lipschitz continuity of the solution mapping to the skorokhod problem, with applications
Paul Dupuis;Hitoshi Ishii.
Stochastics An International Journal of Probability and Stochastic Processes (1991)
Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations
Indiana University Mathematics Journal (1984)
Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains
Yoshikazu Giga;Shun'ichi Goto;Hitoshi Ishii;Moto-hiko Sato.
Preprint Series of Department of Mathematics, Hokkaido University (1990)
Approximate solutions of the Bellman equation of deterministic control theory
I. Capuzzo Dolcetta;H. Ishii.
Applied Mathematics and Optimization (1984)
SDEs with Oblique Reflection on Nonsmooth Domains
Paul Dupuis;Hitoshi Ishii.
Annals of Probability (2008)
Hamilton-Jacobi Equations with Discontinuous Hamiltonians on Arbitrary Open Sets
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