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- Hitoshi Ishii

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
35
Citations
12,266
120
World Ranking
1845
National Ranking
29

2013 - Fellow of the American Mathematical Society

- Mathematical analysis
- Partial differential equation
- Geometry

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.

- User’s guide to viscosity solutions of second order partial differential equations (4230 citations)
- Viscosity solutions of fully nonlinear second-order elliptic partial differential equations (484 citations)
- Perron’s method for Hamilton-Jacobi equations (348 citations)

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.

- Mathematical analysis (70.63%)
- Hamilton–Jacobi equation (41.96%)
- Partial differential equation (24.48%)

- Degenerate energy levels (12.59%)
- Mathematical analysis (70.63%)
- Hamilton–Jacobi equation (41.96%)

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.

- A family of degenerate elliptic operators: Maximum principle and its consequences (38 citations)
- The vanishing discount problem and viscosity Mather measures. Part 1: The problem on a torus (30 citations)
- The vanishing discount problem and viscosity Mather measures. Part 2: Boundary value problems (21 citations)

- Mathematical analysis
- Partial differential equation
- Geometry

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.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

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)**

5836 Citations

Viscosity solutions of fully nonlinear second-order elliptic partial differential equations

H Ishii;P.L Lions.

Journal of Differential Equations **(1990)**

673 Citations

Perron’s method for Hamilton-Jacobi equations

Hitoshi Ishii.

Duke Mathematical Journal **(1987)**

507 Citations

On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's

Hitoshi Ishii.

Communications on Pure and Applied Mathematics **(1989)**

432 Citations

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)**

345 Citations

Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations

H. Ishii.

Indiana University Mathematics Journal **(1984)**

264 Citations

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)**

243 Citations

Approximate solutions of the Bellman equation of deterministic control theory

I. Capuzzo Dolcetta;H. Ishii.

Applied Mathematics and Optimization **(1984)**

206 Citations

SDEs with Oblique Reflection on Nonsmooth Domains

Paul Dupuis;Hitoshi Ishii.

Annals of Probability **(2008)**

206 Citations

Hamilton-Jacobi Equations with Discontinuous Hamiltonians on Arbitrary Open Sets

Hitoshi Ishii.

中央大学理工学部紀要 **(1985)**

193 Citations

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