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Hitoshi Ishii

Hitoshi Ishii

D-Index & Metrics

Mathematics

D-Index
41
Citations
13688
World Ranking
1854
National Ranking
26

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society

Overview

Hitoshi Ishii is affiliated with Waseda University in Japan and specializes in mathematics and computer science with a focus on applied mathematics and computational theory. Their research spans several subfields including mechanical and aerospace engineering. The core topics in their work cover nonlinear partial differential equations, geometric analysis and curvature flows, advanced mathematical modeling in engineering, optimization and variational analysis, nonlinear differential equation analysis, spectral theory in mathematical physics, and quantum chaos and dynamical systems.

Among their recent publications are:

  • The vanishing discount problem for Hamilton-Jacobi equations in the Euclidean space, 2020, Communications in Partial Differential Equations
  • Existence through convexity for the truncated Laplacians, 2020, Mathematische Annalen
  • The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: part 2-nonlinear coupling, 2020, Calculus of Variations and Partial Differential Equations
  • The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 1: linear coupling, 2020, Mathematics in Engineering
  • Hamilton-Jacobi equations with their Hamiltonians depending Lipschitz continuously on the unknown, 2021, Communications in Partial Differential Equations

Hitoshi Ishii frequently publishes in several scientific venues, notably:

  • arXiv (Cornell University)
  • Communications in Partial Differential Equations
  • Mathematics in Engineering
  • Mathematische Annalen
  • Calculus of Variations and Partial Differential Equations

Their frequent coauthors include:

  • Isabeau Birindelli
  • Giulio Galise
  • Taiga Kumagai
  • Ariela Briani
  • Kaizhi Wang

Hitoshi Ishii has contributed extensively to the fields of mathematics and computer science, with a portfolio of 45 publications in mathematics and 18 in computer science. Their research includes 35 works in applied mathematics and 12 in computational theory and mathematics.

The scope of their work engages important topics such as:

  • Nonlinear Partial Differential Equations
  • Geometric Analysis and Curvature Flows
  • Advanced Mathematical Modeling in Engineering
  • Optimization and Variational Analysis
  • Nonlinear Differential Equations Analysis
  • Spectral Theory in Mathematical Physics
  • Quantum chaos and dynamical systems

In recognition of their contributions, Hitoshi Ishii was named a Fellow of the American Mathematical Society in 2013.

Best Publications

  • User’s guide to viscosity solutions of second order partial differential equations

    Michael G. Crandall;Hitoshi Ishii;Pierre Louis Lions

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

    H Ishii;P.L Lions

  • Perron’s method for Hamilton-Jacobi equations

    Hitoshi Ishii

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

    Hitoshi Ishii

  • On lipschitz continuity of the solution mapping to the skorokhod problem, with applications

    Paul Dupuis;Hitoshi Ishii

  • Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations

    H. Ishii

  • Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains

    Yoshikazu Giga;Shun'ichi Goto;Hitoshi Ishii;Moto-hiko Sato

  • SDEs with Oblique Reflection on Nonsmooth Domains

    Paul Dupuis;Hitoshi Ishii

  • Approximate solutions of the Bellman equation of deterministic control theory

    I. Capuzzo Dolcetta;H. Ishii

  • Hamilton-Jacobi Equations with Discontinuous Hamiltonians on Arbitrary Open Sets

    Hitoshi Ishii

  • The maximum principle for semicontinuous functions

    Michael G. Crandall;Hitoshi Ishii

  • A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations

    Hitoshi Ishii

  • Asymptotic stability and blowing up of solutions of some nonlinear equations

    Hitoshi Ishii

  • Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited

    Michael G. Crandall;Hitoshi Ishii;Pierre Louis Lions

  • A simple, direct proof of uniqueness for solutions of the hamilton-jacobi equations of eikonal type

    Hitoshi Ishii

  • Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor

    Hitoshi Ishii;Panagiotis Souganidis

  • Viscosity solutions for monotone systems of second-order elliptic PDES

    Hitoshi Ishii;Shigeaki Koike

  • A class of integral equations and approximation of p-Laplace equations

    Hitoshi Ishii;Gou Nakamura

  • Asymptotic solutions for large time of Hamilton–Jacobi equations in Euclidean n space

    Hitoshi Ishii

  • A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities

    L.C. Evans;H. Ishii

Frequent Co-Authors

Panagiotis E. Souganidis
Panagiotis E. Souganidis University of Chicago
Pierre-Louis Lions
Pierre-Louis Lions Collège de France
Paul Dupuis
Paul Dupuis Brown University
Michael G. Crandall
Michael G. Crandall University of California, Santa Barbara
Guy Barles
Guy Barles François Rabelais University
Yoshikazu Giga
Yoshikazu Giga University of Tokyo
Lawrence C. Evans
Lawrence C. Evans University of California, Berkeley
H. Mete Soner
H. Mete Soner Princeton University

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