What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- 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)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Mathematical analysis (70.63%)
- Hamilton–Jacobi equation (41.96%)
- Partial differential equation (24.48%)
What were the highlights of his more recent work (between 2015-2021)?
- Degenerate energy levels (12.59%)
- Mathematical analysis (70.63%)
- Hamilton–Jacobi equation (41.96%)
In recent papers he was focusing on the following fields of study:
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.
Between 2015 and 2021, his most popular works were:
- 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)
In his most recent research, the most cited papers focused on:
- 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.
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