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## Ishii, Hitoshi

Compute Distance To:
 Author ID: ishii.hitoshi Published as: Ishii, H.; Ishii, Hitoshi Homepage: http://www.edu.waseda.ac.jp/~ishii/ External Links: Wikidata · dblp · GND
 Documents Indexed: 142 Publications since 1973, including 3 Books
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#### Co-Authors

 46 single-authored 8 Koike, Shigeaki 8 Loreti, Paola 6 Dupuis, Paul G. 6 Mitake, Hiroyoshi 6 Souganidis, Panagiotis E. 5 Lions, Pierre-Louis 5 Mikami, Toshio 4 Giga, Yoshikazu 3 Arisawa, Mariko 3 Birindelli, Isabeau 3 Capuzzo Dolcetta, Italo 3 Crandall, Michael G. 3 Fujita, Yasuhiro 3 Galise, Giulio 3 Ichihara, Naoyuki 3 Sato, Moto-Hiko 3 Tran Vinh Hung 2 Alvarez, Orlando 2 Alzahrani, Ebraheem O. 2 Barles, Guy 2 Barron, Emmanuel Nicholas 2 Evans, Lawrence Christopher 2 Evans, Lawrence Craig 2 Goto, Shun’ichi 2 Horie, Kazuo 2 Ikoma, Norihisa 2 Takagi, Izumi 2 Tsutsumi, Masayoshi 2 Younas, Arshad Mahmood M. 1 Adalsteinsson, David 1 Al-Aidarous, Eman Salem 1 Alaidarous, Eman S. 1 Bardi, Martino 1 Biswas, Anup 1 Chen, Qinbo 1 Cheng, Wei 1 Chopp, David L. 1 Du, Yihong 1 Fukuda, Isamu 1 Goatin, Paola 1 Ishii, Katsuyuki 1 Jin, Liang 1 Kenmochi, Nobuyuki 1 Kobayasi, Kazuo 1 Kumagai, Taiga 1 Lin, Wei-Yueh 1 Matsumura, Yutaka 1 Menaldi, Jose-Luis 1 Nagai, Hideo 1 Nakamitsu, Kuniaki 1 Nakamura, Gou 1 Pires, Gabriel E. 1 Ramaswamy, Mythily 1 Sagisaka, Yoshinori 1 Saha, Subhamay 1 Shimano, Kazufumi 1 Siconolfi, Antonio 1 Soner, Halil Mete 1 Teramoto, Fuyuhiko 1 Tessitore, Maria Elisabetta 1 Wang, Lin 1 Yamada, Naoki Yamada 1 Zaremba, Leszek S. 1 Zhao, Kai
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#### Serials

 11 Indiana University Mathematics Journal 10 Communications in Partial Differential Equations 7 RIMS Kokyuroku 5 Funkcialaj Ekvacioj. Serio Internacia 5 Journal of Differential Equations 5 Bulletin of the Faculty of Science and Engineering. Series I. Mathematics 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Differential and Integral Equations 5 SIAM Journal on Mathematical Analysis 5 Calculus of Variations and Partial Differential Equations 4 Archive for Rational Mechanics and Analysis 4 Nonlinear Analysis. Theory, Methods & Applications 3 The Annals of Probability 3 Applied Mathematics and Optimization 3 Mathematica Japonica 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Discrete and Continuous Dynamical Systems 2 Duke Mathematical Journal 2 Journal of the Mathematical Society of Japan 2 SIAM Journal on Control and Optimization 2 Advances in Mathematical Sciences and Applications 2 Bulletin of Mathematical Sciences 1 Advances in Applied Probability 1 Applicable Analysis 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Biology 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Hokkaido Mathematical Journal 1 Journal of Functional Analysis 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Tohoku Mathematical Journal. Second Series 1 Transactions of the American Mathematical Society 1 Zeitschrift für Analysis und ihre Anwendungen 1 Revista Matemática Iberoamericana 1 Sugaku Expositions 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Problems of Control and Information Theory 1 Bulletin of the American Mathematical Society. New Series 1 Stochastics and Stochastics Reports 1 Methods and Applications of Analysis 1 Advances in Differential Equations 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Proceedings of the Japan Academy
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#### Fields

 120 Partial differential equations (35-XX) 57 Calculus of variations and optimal control; optimization (49-XX) 11 Dynamical systems and ergodic theory (37-XX) 10 Probability theory and stochastic processes (60-XX) 10 Mechanics of particles and systems (70-XX) 7 Differential geometry (53-XX) 6 General and overarching topics; collections (00-XX) 5 Systems theory; control (93-XX) 4 Ordinary differential equations (34-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Integral equations (45-XX) 2 Numerical analysis (65-XX) 2 Biology and other natural sciences (92-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH

114 Publications have been cited 3,789 times in 2,511 Documents Cited by Year
User’s guide to viscosity solutions of second order partial differential equations. Zbl 0755.35015
Crandall, Michael G.; Ishii, Hitoshi; Lions, Pierre-Louis
1992
Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. Zbl 0708.35031
Ishii, H.; Lions, P. L.
1990
Perron’s method for Hamilton-Jacobi equations. Zbl 0697.35030
Ishii, Hitoshi
1987
On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE’s. Zbl 0645.35025
Ishii, Hitoshi
1989
On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Zbl 0721.60062
Dupuis, Paul; Ishii, Hitoshi
1991
Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains. Zbl 0836.35009
Giga, Y.; Goto, S.; Ishii, H.; Sato, M.-H.
1991
Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations. Zbl 0551.49016
Ishii, Hitoshi
1984
Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets. Zbl 0937.35505
Ishii, Hitoshi
1985
SDEs with oblique reflection on nonsmooth domains. Zbl 0787.60099
Dupuis, Paul; Ishii, Hitoshi
1993
Viscosity solutions for monotone systems of second order elliptic PDEs. Zbl 0742.35022
Ishii, Hitoshi; Koike, Shigeaki
1991
Asymptotic stability and blowing up of solutions of some nonlinear equations. Zbl 0339.34062
Ishii, Hitoshi
1977
A class of integral equations and approximation of $$p$$-Laplace equations. Zbl 1198.45005
Ishii, Hitoshi; Nakamura, Gou
2010
A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations. Zbl 0701.35052
Ishii, Hitoshi
1989
Approximate solutions of the Bellman equation of deterministic control theory. Zbl 0553.49024
Capuzzo Dolcetta, I.; Ishii, H.
1984
The Bellman equation for minimizing the maximum cost. Zbl 0691.49030
Barron, E. N.; Ishii, H.
1989
A simple, direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of eikonal type. Zbl 0644.35017
Ishii, Hitoshi
1987
Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor. Zbl 0837.35066
Ishii, Hitoshi; Souganidis, Panagiotis
1995
On the equivalence of two notions of weak solutions, viscosity solutions and distribution solutions. Zbl 0833.35053
Ishii, Hitoshi
1995
A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities. Zbl 0601.60076
Evans, L. C.; Ishii, H.
1985
Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited. Zbl 0644.35016
Crandall, Michael G.; Ishii, Hitoshi; Lions, Pierre-Louis
1987
The maximum principle for semicontinuous functions. Zbl 0723.35015
Crandall, Michael G.; Ishii, Hitoshi
1990
Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean $$n$$ space. Zbl 1145.35035
Ishii, Hitoshi
2008
A new formulation of state constraint problems for first-order PDEs. Zbl 0847.49025
Ishii, Hitoshi; Koike, Shigeaki
1996
Almost periodic homogenization of Hamilton-Jacobi equations. Zbl 0969.35018
Ishii, Hitoshi
2000
Threshold dynamics type approximation schemes for propagating fronts. Zbl 0935.53006
Ishii, Hitoshi; Pires, Gabriel E.; Souganidis, Panagiotis E.
1999
Viscosity solutions of a system of nonlinear second-order elliptic PDEs arising in switching games. Zbl 0789.35062
Ishii, Hitoshi; Koike, Shigeaki
1991
Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians. Zbl 1136.35016
Ishii, Hitoshi; Mitake, Hiroyoshi
2007
Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE’s. Zbl 0733.35020
Ishii, Hitoshi
1991
A viscosity solution approach to the asymptotic analysis of queueing systems. Zbl 0715.60035
Dupuis, Paul; Ishii, Hitoshi; Soner, H. Meté
1990
Existence and uniqueness of solutions of Hamilton-Jacobi equations. Zbl 0614.35011
Ishii, Hitoshi
1986
Boundary regularity and uniqueness for an elliptic equation with gradient constraint. Zbl 0538.35012
Ishii, Hitoshi; Koike, Shigeaki
1983
Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $$n$$ space. Zbl 1112.35041
Fujita, Yasuhiro; Ishii, Hitoshi; Loreti, Paola
2006
Hopf-Lax formulas for semicontinuous data. Zbl 0939.35045
Alvarez, O.; Barron, E. N.; Ishii, H.
1999
Viscosity solutions for a class of Hamilton-Jacobi equations in Hilbert spaces. Zbl 0753.70014
Ishii, Hitoshi
1992
A family of degenerate elliptic operators: maximum principle and its consequences. Zbl 1390.35079
Birindelli, Isabeau; Galise, Giulio; Ishii, Hitoshi
2018
On the rate of convergence in homogenization of Hamilton-Jacobi equations. Zbl 1256.35003
Capuzzo-Dolcetta, I.; Ishii, H.
2001
On oblique derivative problems for fully nonlinear second-order elliptic partial differential equations on nonsmooth domains. Zbl 0736.35044
Dupuis, Paul; Ishii, Hitoshi
1990
Global existence of weak solutions for interface equations coupled with diffusion equations. Zbl 0754.35061
Giga, Yoshikazu; Goto, Shun’ichi; Ishii, Hitoshi
1992
On oblique derivative problems for fully nonlinear second-order elliptic PDE’s on domains with corners. Zbl 0741.35019
Dupuis, Paul; Ishii, Hitoshi
1991
Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics. Zbl 0501.92020
Ishii, Hitoshi; Takagi, Izumi
1982
Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians. Zbl 1243.70017
Ichihara, Naoyuki; Ishii, Hitoshi
2009
Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians. Zbl 1145.35034
Ichihara, Naoyuki; Ishii, Hitoshi
2008
Remarks on existence of viscosity solutions of Hamilton-Jacobi equations. Zbl 0546.35042
Ishii, Hitoshi
1983
Viscosity solutions of nonlinear second-order partial differential equations in Hilbert spaces. Zbl 0812.35153
Ishii, Hitoshi
1993
The vanishing discount problem and viscosity Mather measures. 1: The problem on a torus. Zbl 1375.35182
Ishii, Hitoshi; Mitake, Hiroyoshi; Tran, Hung V.
2017
Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator. Zbl 1101.35017
Fujita, Yasuhiro; Ishii, Hitoshi; Loreti, Paola
2006
Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. Zbl 1055.35066
Ishii, Hitoshi; Sato, Moto-Hiko
2004
A generalization of the Bence, Merriman and Osher algorithm for motion by mean curvature. Zbl 0844.35043
Ishii, Hitoshi
1995
Differential games and nonlinear first order PDE on bounded domains. Zbl 0559.35013
Evans, L. C.; Ishii, H.
1984
On the existence of almost periodic complete trajectories for contractive almost periodic processes. Zbl 0523.34047
Ishii, Hitoshi
1982
Perron’s method for monotone systems of second-order elliptic partial differential equations. Zbl 0770.35017
Ishii, Hitoshi
1992
Remarks on elliptic singular perturbation problems. Zbl 0724.35009
Ishii, Hitoshi; Koike, Shigeaki
1991
Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions. Zbl 1222.35031
Ishii, Hitoshi
2011
Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions. Zbl 1213.35184
Ishii, Hitoshi
2011
Representation of solutions of Hamilton-Jacobi equations. Zbl 0687.35025
Ishii, Hitoshi
1988
A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations. Zbl 1269.49044
Ishii, Hitoshi
2013
Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients. Zbl 0842.35019
Ishii, Hitoshi; Ramaswamy, Mythily
1995
The vanishing discount problem and viscosity Mather measures. II: Boundary value problems. Zbl 1375.35183
Ishii, Hitoshi; Mitake, Hiroyoshi; Tran, Hung V.
2017
A convergence result for the ergodic problem for Hamilton-Jacobi equations with Neumann-type boundary conditions. Zbl 1350.35063
Al-Aidarous, Eman S.; Alzahrani, Ebraheem O.; Ishii, Hitoshi; Younas, Arshad M. M.
2016
A new PDE approach to the large time asymptotics of solutions of Hamilton-Jacobi equations. Zbl 1284.35065
Barles, Guy; Ishii, Hitoshi; Mitake, Hiroyoshi
2013
The large-time behavior of solutions of Hamilton-Jacobi equations on the real line. Zbl 1170.35339
Ichihara, Naoyuki; Ishii, Hitoshi
2008
Homogenization of the Cauchy problem for Hamilton-Jacobi equations. Zbl 0918.49024
Ishii, Hitoshi
1999
On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions. Zbl 1282.70037
Barles, Guy; Ishii, Hitoshi; Mitake, Hiroyoshi
2012
A PDE approach to small stochastic perturbations of Hamiltonian flows. Zbl 1287.37036
Ishii, Hitoshi; Souganidis, Panagiotis E.
2012
A class stochastic optimal control problems with state constraint. Zbl 1049.93091
Ishii, Hitoshi; Loreti, Paola
2002
Hamilton-Jacobi equations with partial gradient and application to homogenization. Zbl 1014.49021
Alvarez, O.; Ishii, H.
2001
Homogenization of Hamilton-Jacobi equations on domains with small scale periodic structure. Zbl 0924.49020
Horie, Kazuo; Ishii, Hitoshi
1998
Comparison results for Hamilton-Jacobi equations without growth condition on solutions from above. Zbl 0894.35021
Ishii, Hitoshi
1997
Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls. Zbl 1254.35166
Ikoma, Norihisa; Ishii, Hitoshi
2012
On some Fourier multipliers and partial differential equations. Zbl 0321.35022
Ishii, Hitoshi
1974
Vanishing contact structure problem and convergence of the viscosity solutions. Zbl 1437.35155
Chen, Qinbo; Cheng, Wei; Ishii, Hitoshi; Zhao, Kai
2019
Asymptotic analysis for the eikonal equation with the dynamical boundary conditions. Zbl 1304.35046
Al-Aidarous, Eman S.; Alzahrani, Ebraheem O.; Ishii, Hitoshi; Younas, Arshad M. M.
2014
Uniqueness of solutions to the Cauchy problem for $$u_ t-u\Delta u+\gamma|\nabla u|^ 2=0$$. Zbl 0806.35063
Fukuda, Isamu; Ishii, Hitoshi; Tsutsumi, Masayoshi
1993
On a certain estimate of the free boundary in the Stefan problem. Zbl 0476.35082
Ishii, Hitoshi
1981
Asymptotic stability and existence of almost periodic solutions for the one-dimensional two-phase Stefan problem. Zbl 0468.35009
Ishii, Hitoshi
1980
SDEs with oblique reflections on nonsmooth domains. Zbl 1168.60019
Dupuis, Paul; Ishii, Hitoshi
2008
Limits of solutions of $$p$$-Laplace equations as $$p$$ goes to infinity and related variational problems. Zbl 1134.35307
Ishii, Hitoshi; Loreti, Paola
2005
Simultaneous effects of homogenization and vanishing viscosity in fully nonlinear elliptic equations. Zbl 1151.35351
Horie, Kazuo; Ishii, Hitoshi
2003
Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics. Zbl 1185.35022
Ishii, Hitoshi
2008
Asymptotic solutions for large time of Hamilton–Jacobi equations. Zbl 1098.35029
Ishii, Hitoshi
2006
Relaxation in an $$L^ \infty$$-optimization problem. Zbl 1042.49013
Ishii, Hitoshi; Loreti, Paola
2003
On $$\varepsilon$$-optimal controls for state constraint problems. Zbl 0969.49019
Ishii, Hitoshi; Koike, Shigeaki
2000
A Dirichlet type problem for nonlinear degenerate elliptic equations arising in time-optimal stochastic control. Zbl 0970.35065
Bardi, Martino; Goatin, Paola; Ishii, Hitoshi
2000
Waiting time effects for Gauss curvature flows. Zbl 0995.53050
Chopp, D.; Evans, L. C.; Ishii, H.
1999
Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces. Zbl 0841.35057
Ishii, Hitoshi
1996
Viscosity solutions of nonlinear partial differential equations. Zbl 0968.35002
Ishii, Hitoshi
1994
Viscosity solutions of functional differential equations. Zbl 0818.35131
Ishii, Hitoshi; Koike, Shigeaki
1994
On viscosity solution of HJB equations with state constraints and reflection control. Zbl 1354.93172
Biswas, Anup; Ishii, Hitoshi; Saha, Subhamay; Wang, Lin
2017
Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls. II. Zbl 1331.35253
Ikoma, Norihisa; Ishii, Hitoshi
2015
Metastability for parabolic equations with drift. I. Zbl 1327.35140
Ishii, Hitoshi; Souganidis, Panagiotis E.
2015
Non-local Hamilton-Jacobi equations arising in dislocation dynamics. Zbl 1207.35097
Ishii, Hitoshi; Matsumura, Yutaka
2010
Convexified Gauss curvature flow of sets: a stochastic approximation. Zbl 1129.53048
Ishii, Hitoshi; Mikami, Toshio
2004
A level set approach to the wearing process of a nonconvex stone. Zbl 1114.53060
Ishii, Hitoshi; Mikami, Toshio
2004
Relaxation of Hamilton-Jacobi equations. Zbl 1036.70011
Ishii, Hitoshi; Loreti, Paola
2003
A generalization of a theorem of Barron and Jensen and a comparison theorem for lower semicontinuous viscosity solutions. Zbl 1158.49302
Ishii, Hitoshi
2001
On the rate of convergence in homogenization of Hamilton-Jacobi equations. Zbl 0968.49019
Capuzzo Dolcetta, I.; Ishii, H.
2000
A characterization of the existence of solutions for Hamilton-Jacobi equations in ergodic control problems with applications. Zbl 0967.35029
Arisawa, M.; Ishii, H.; Lions, P.-L.
2000
A singular limit on risk sensitive control and semi-classical analysis. Zbl 0963.93081
Ishii, Hitoshi; Nagai, Hideo; Teramoto, Fuyuhiko
1996
On the uniqueness and existence of solutions of fully nonlinear parabolic PDEs under the Osgood type condition. Zbl 0811.35051
Ishii, H.; Kobayasi, K.
1994
A remark on a system of inequalities with bilateral obstacles. Zbl 0718.49010
1989
Towards a reversed Faber-Krahn inequality for the truncated Laplacian. Zbl 1445.35158
Birindelli, Isabeau; Galise, Giulio; Ishii, Hitoshi
2020
The vanishing discount problem for Hamilton-Jacobi equations in the Euclidean space. Zbl 1442.35032
Ishii, Hitoshi; Siconolfi, Antonio
2020
Vanishing contact structure problem and convergence of the viscosity solutions. Zbl 1437.35155
Chen, Qinbo; Cheng, Wei; Ishii, Hitoshi; Zhao, Kai
2019
A family of degenerate elliptic operators: maximum principle and its consequences. Zbl 1390.35079
Birindelli, Isabeau; Galise, Giulio; Ishii, Hitoshi
2018
The vanishing discount problem and viscosity Mather measures. 1: The problem on a torus. Zbl 1375.35182
Ishii, Hitoshi; Mitake, Hiroyoshi; Tran, Hung V.
2017
The vanishing discount problem and viscosity Mather measures. II: Boundary value problems. Zbl 1375.35183
Ishii, Hitoshi; Mitake, Hiroyoshi; Tran, Hung V.
2017
On viscosity solution of HJB equations with state constraints and reflection control. Zbl 1354.93172
Biswas, Anup; Ishii, Hitoshi; Saha, Subhamay; Wang, Lin
2017
Metastability for parabolic equations with drift. II: The quasilinear case. Zbl 1387.35052
Ishii, Hitoshi; Souganidis, Panagiotis E.
2017
A convergence result for the ergodic problem for Hamilton-Jacobi equations with Neumann-type boundary conditions. Zbl 1350.35063
Al-Aidarous, Eman S.; Alzahrani, Ebraheem O.; Ishii, Hitoshi; Younas, Arshad M. M.
2016
Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls. II. Zbl 1331.35253
Ikoma, Norihisa; Ishii, Hitoshi
2015
Metastability for parabolic equations with drift. I. Zbl 1327.35140
Ishii, Hitoshi; Souganidis, Panagiotis E.
2015
Asymptotic analysis for the eikonal equation with the dynamical boundary conditions. Zbl 1304.35046
Al-Aidarous, Eman S.; Alzahrani, Ebraheem O.; Ishii, Hitoshi; Younas, Arshad M. M.
2014
A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations. Zbl 1269.49044
Ishii, Hitoshi
2013
A new PDE approach to the large time asymptotics of solutions of Hamilton-Jacobi equations. Zbl 1284.35065
Barles, Guy; Ishii, Hitoshi; Mitake, Hiroyoshi
2013
On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions. Zbl 1282.70037
Barles, Guy; Ishii, Hitoshi; Mitake, Hiroyoshi
2012
A PDE approach to small stochastic perturbations of Hamiltonian flows. Zbl 1287.37036
Ishii, Hitoshi; Souganidis, Panagiotis E.
2012
Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls. Zbl 1254.35166
Ikoma, Norihisa; Ishii, Hitoshi
2012
Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions. Zbl 1222.35031
Ishii, Hitoshi
2011
Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions. Zbl 1213.35184
Ishii, Hitoshi
2011
A class of integral equations and approximation of $$p$$-Laplace equations. Zbl 1198.45005
Ishii, Hitoshi; Nakamura, Gou
2010
Non-local Hamilton-Jacobi equations arising in dislocation dynamics. Zbl 1207.35097
Ishii, Hitoshi; Matsumura, Yutaka
2010
Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians. Zbl 1243.70017
Ichihara, Naoyuki; Ishii, Hitoshi
2009
Two remarks on periodic solutions of Hamilton-Jacobi equations. Zbl 1184.35017
Ishii, Hitoshi; Mitake, Hiroyoshi
2009
Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean $$n$$ space. Zbl 1145.35035
Ishii, Hitoshi
2008
Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians. Zbl 1145.35034
Ichihara, Naoyuki; Ishii, Hitoshi
2008
The large-time behavior of solutions of Hamilton-Jacobi equations on the real line. Zbl 1170.35339
Ichihara, Naoyuki; Ishii, Hitoshi
2008
SDEs with oblique reflections on nonsmooth domains. Zbl 1168.60019
Dupuis, Paul; Ishii, Hitoshi
2008
Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics. Zbl 1185.35022
Ishii, Hitoshi
2008
Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians. Zbl 1136.35016
Ishii, Hitoshi; Mitake, Hiroyoshi
2007
Asymptotic solutions of Hamilton-Jacobi equations in Euclidean $$n$$ space. Zbl 1112.35041
Fujita, Yasuhiro; Ishii, Hitoshi; Loreti, Paola
2006
Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator. Zbl 1101.35017
Fujita, Yasuhiro; Ishii, Hitoshi; Loreti, Paola
2006
Asymptotic solutions for large time of Hamilton–Jacobi equations. Zbl 1098.35029
Ishii, Hitoshi
2006
Limits of solutions of $$p$$-Laplace equations as $$p$$ goes to infinity and related variational problems. Zbl 1134.35307
Ishii, Hitoshi; Loreti, Paola
2005
Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. Zbl 1055.35066
Ishii, Hitoshi; Sato, Moto-Hiko
2004
Convexified Gauss curvature flow of sets: a stochastic approximation. Zbl 1129.53048
Ishii, Hitoshi; Mikami, Toshio
2004
A level set approach to the wearing process of a nonconvex stone. Zbl 1114.53060
Ishii, Hitoshi; Mikami, Toshio
2004
Simultaneous effects of homogenization and vanishing viscosity in fully nonlinear elliptic equations. Zbl 1151.35351
Horie, Kazuo; Ishii, Hitoshi
2003
Relaxation in an $$L^ \infty$$-optimization problem. Zbl 1042.49013
Ishii, Hitoshi; Loreti, Paola
2003
Relaxation of Hamilton-Jacobi equations. Zbl 1036.70011
Ishii, Hitoshi; Loreti, Paola
2003
Asymptotic analysis for a class of infinite systems of first-order PDE: nonlinear parabolic PDE in the singular limit. Zbl 1040.35128
Ishii, Hitoshi; Shimano, Kazufumi
2003
A class stochastic optimal control problems with state constraint. Zbl 1049.93091
Ishii, Hitoshi; Loreti, Paola
2002
A two-dimensional random crystalline algorithm for Gauss curvature flow. Zbl 1026.60009
Ishii, H.; Mikami, T.
2002
On the rate of convergence in homogenization of Hamilton-Jacobi equations. Zbl 1256.35003
Capuzzo-Dolcetta, I.; Ishii, H.
2001
Hamilton-Jacobi equations with partial gradient and application to homogenization. Zbl 1014.49021
Alvarez, O.; Ishii, H.
2001
A generalization of a theorem of Barron and Jensen and a comparison theorem for lower semicontinuous viscosity solutions. Zbl 1158.49302
Ishii, Hitoshi
2001
A mathematical model of the wearing process of a nonconvex stone. Zbl 1033.53059
Ishii, Hitoshi; Mikami, Toshio
2001
An approximation scheme for motion by mean curvature with right-angle boundary condition. Zbl 0994.35012
Ishii, Hitoshi; Ishii, Katsuyuki
2001
Almost periodic homogenization of Hamilton-Jacobi equations. Zbl 0969.35018
Ishii, Hitoshi
2000
On $$\varepsilon$$-optimal controls for state constraint problems. Zbl 0969.49019
Ishii, Hitoshi; Koike, Shigeaki
2000
A Dirichlet type problem for nonlinear degenerate elliptic equations arising in time-optimal stochastic control. Zbl 0970.35065
Bardi, Martino; Goatin, Paola; Ishii, Hitoshi
2000
On the rate of convergence in homogenization of Hamilton-Jacobi equations. Zbl 0968.49019
Capuzzo Dolcetta, I.; Ishii, H.
2000
A characterization of the existence of solutions for Hamilton-Jacobi equations in ergodic control problems with applications. Zbl 0967.35029
Arisawa, M.; Ishii, H.; Lions, P.-L.
2000
Gauss curvature flow and its approximation. Zbl 0987.53027
Ishii, Hitoshi
2000
Threshold dynamics type approximation schemes for propagating fronts. Zbl 0935.53006
Ishii, Hitoshi; Pires, Gabriel E.; Souganidis, Panagiotis E.
1999
Hopf-Lax formulas for semicontinuous data. Zbl 0939.35045
Alvarez, O.; Barron, E. N.; Ishii, H.
1999
Homogenization of the Cauchy problem for Hamilton-Jacobi equations. Zbl 0918.49024
Ishii, Hitoshi
1999
Waiting time effects for Gauss curvature flows. Zbl 0995.53050
Chopp, D.; Evans, L. C.; Ishii, H.
1999
Hopf-Lax formulas for Hamilton-Jacobi equations with semicontinuous initial data. Zbl 0957.35503
Ishii, Hitoshi
1999
Homogenization of Hamilton-Jacobi equations on domains with small scale periodic structure. Zbl 0924.49020
Horie, Kazuo; Ishii, Hitoshi
1998
Comparison results for Hamilton-Jacobi equations without growth condition on solutions from above. Zbl 0894.35021
Ishii, Hitoshi
1997
The level set method for etching and deposition. Zbl 0924.35029
Adalsteinsson, D.; Evans, L. C.; Ishii, H.
1997
A new formulation of state constraint problems for first-order PDEs. Zbl 0847.49025
Ishii, Hitoshi; Koike, Shigeaki
1996
Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces. Zbl 0841.35057
Ishii, Hitoshi
1996
A singular limit on risk sensitive control and semi-classical analysis. Zbl 0963.93081
Ishii, Hitoshi; Nagai, Hideo; Teramoto, Fuyuhiko
1996
Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor. Zbl 0837.35066
Ishii, Hitoshi; Souganidis, Panagiotis
1995
On the equivalence of two notions of weak solutions, viscosity solutions and distribution solutions. Zbl 0833.35053
Ishii, Hitoshi
1995
A generalization of the Bence, Merriman and Osher algorithm for motion by mean curvature. Zbl 0844.35043
Ishii, Hitoshi
1995
Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients. Zbl 0842.35019
Ishii, Hitoshi; Ramaswamy, Mythily
1995
Viscosity solutions and their applications. Zbl 0969.35021
Ishii, Hitoshi
1995
Viscosity solutions of nonlinear partial differential equations. Zbl 0968.35002
Ishii, Hitoshi
1994
Viscosity solutions of functional differential equations. Zbl 0818.35131
Ishii, Hitoshi; Koike, Shigeaki
1994
On the uniqueness and existence of solutions of fully nonlinear parabolic PDEs under the Osgood type condition. Zbl 0811.35051
Ishii, H.; Kobayasi, K.
1994
SDEs with oblique reflection on nonsmooth domains. Zbl 0787.60099
Dupuis, Paul; Ishii, Hitoshi
1993
Viscosity solutions of nonlinear second-order partial differential equations in Hilbert spaces. Zbl 0812.35153
Ishii, Hitoshi
1993
Uniqueness of solutions to the Cauchy problem for $$u_ t-u\Delta u+\gamma|\nabla u|^ 2=0$$. Zbl 0806.35063
Fukuda, Isamu; Ishii, Hitoshi; Tsutsumi, Masayoshi
1993
User’s guide to viscosity solutions of second order partial differential equations. Zbl 0755.35015
Crandall, Michael G.; Ishii, Hitoshi; Lions, Pierre-Louis
1992
Viscosity solutions for a class of Hamilton-Jacobi equations in Hilbert spaces. Zbl 0753.70014
Ishii, Hitoshi
1992
Global existence of weak solutions for interface equations coupled with diffusion equations. Zbl 0754.35061
Giga, Yoshikazu; Goto, Shun’ichi; Ishii, Hitoshi
1992
Perron’s method for monotone systems of second-order elliptic partial differential equations. Zbl 0770.35017
Ishii, Hitoshi
1992
On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Zbl 0721.60062
Dupuis, Paul; Ishii, Hitoshi
1991
Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains. Zbl 0836.35009
Giga, Y.; Goto, S.; Ishii, H.; Sato, M.-H.
1991
Viscosity solutions for monotone systems of second order elliptic PDEs. Zbl 0742.35022
Ishii, Hitoshi; Koike, Shigeaki
1991
Viscosity solutions of a system of nonlinear second-order elliptic PDEs arising in switching games. Zbl 0789.35062
Ishii, Hitoshi; Koike, Shigeaki
1991
Fully nonlinear oblique derivative problems for nonlinear second-order elliptic PDE’s. Zbl 0733.35020
Ishii, Hitoshi
1991
On oblique derivative problems for fully nonlinear second-order elliptic PDE’s on domains with corners. Zbl 0741.35019
Dupuis, Paul; Ishii, Hitoshi
1991
Remarks on elliptic singular perturbation problems. Zbl 0724.35009
Ishii, Hitoshi; Koike, Shigeaki
1991
Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. Zbl 0708.35031
Ishii, H.; Lions, P. L.
1990
The maximum principle for semicontinuous functions. Zbl 0723.35015
Crandall, Michael G.; Ishii, Hitoshi
1990
A viscosity solution approach to the asymptotic analysis of queueing systems. Zbl 0715.60035
Dupuis, Paul; Ishii, Hitoshi; Soner, H. Meté
1990
On oblique derivative problems for fully nonlinear second-order elliptic partial differential equations on nonsmooth domains. Zbl 0736.35044
Dupuis, Paul; Ishii, Hitoshi
1990
On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE’s. Zbl 0645.35025
Ishii, Hitoshi
1989
A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations. Zbl 0701.35052
Ishii, Hitoshi
1989
The Bellman equation for minimizing the maximum cost. Zbl 0691.49030
Barron, E. N.; Ishii, H.
1989
A remark on a system of inequalities with bilateral obstacles. Zbl 0718.49010
1989
Representation of solutions of Hamilton-Jacobi equations. Zbl 0687.35025
Ishii, Hitoshi
1988
Perron’s method for Hamilton-Jacobi equations. Zbl 0697.35030
Ishii, Hitoshi
1987
A simple, direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of eikonal type. Zbl 0644.35017
Ishii, Hitoshi
1987
Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited. Zbl 0644.35016
Crandall, Michael G.; Ishii, Hitoshi; Lions, Pierre-Louis
1987
Existence and uniqueness of solutions of Hamilton-Jacobi equations. Zbl 0614.35011
Ishii, Hitoshi
1986
Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets. Zbl 0937.35505
Ishii, Hitoshi
1985
...and 14 more Documents
all top 5

#### Cited by 2,296 Authors

 52 Ishii, Hitoshi 44 Barles, Guy 44 Rossi, Julio Daniel 42 Souganidis, Panagiotis E. 32 Lions, Pierre-Louis 29 Barron, Emmanuel Nicholas 29 Giga, Yoshikazu 28 Mitake, Hiroyoshi 25 Cardaliaguet, Pierre 23 Tran Vinh Hung 21 Quaas, Alexander 21 Soner, Halil Mete 21 Świȩch, Andrzej 19 Monneau, Régis 19 Vitolo, Antonio 18 Buckdahn, Rainer 18 Ley, Olivier 17 Camilli, Fabio 17 Sirakov, Boyan Slavchev 16 Armstrong, Scott N. 16 Capuzzo Dolcetta, Italo 16 Imbert, Cyril 16 Topp, Erwin 16 Touzi, Nizar 15 Bardi, Martino 15 Bayraktar, Erhan 15 Crandall, Michael G. 15 Jakobsen, Espen Robstad 15 Kim, Inwon Christina 15 Koike, Shigeaki 15 Li, Juan 15 Zhang, Jianfeng 14 Caffarelli, Luis Ángel 14 Cannarsa, Piermarco 14 Chasseigne, Emmanuel 14 Oberman, Adam M. 14 Perthame, Benoît 13 Birindelli, Isabeau 13 Bouchard, Bruno 13 Dupuis, Paul G. 13 Felmer, Patricio L. 13 Manfredi, Juan J. 13 Pham, Huyên 12 Falcone, Maurizio 12 Liu, Qing 12 Ma, Jin 12 Peng, Shige 12 Yu, Yifeng 12 Zidani, Hasnaa 11 Chambolle, Antonin 11 Harvey, Reese 11 Juutinen, Petri 11 Siconolfi, Antonio 11 Soravia, Pierpaolo 11 Teixeira, Eduardo V. O. 10 Da Lio, Francesca 10 Dai, Limei 10 Forsyth, Peter A. 10 Gozzi, Fausto 10 Kawohl, Bernd 10 Lindgren, Erik 10 Novaga, Matteo 10 Picarelli, Athena 10 Porretta, Alessio 10 Quincampoix, Marc 10 Torres Ledesma, César Enrique 10 Wang, Changyou 9 Bhattacharya, Tilak 9 Bian, Baojun 9 Budhiraja, Amarjit S. 9 Feng, Xiaobing 9 Forcadel, Nicolas 9 Frankowska, Hélène 9 Gomes, Diogo Luís Aguiar 9 Ishige, Kazuhiro 9 Katzourakis, Nikolaos I. 9 Laurençot, Philippe 9 Lawson, Herbert Blaine jun. 9 Leoni, Fabiana 9 Nadirashvili, Nikolai S. 9 Neilan, Michael 9 Parviainen, Mikko 9 Serea, Oana-Silvia 9 Silvestre, Luis E. 9 Vazquez, Juan Luis 9 Vlǎduţ, Sergei Georgievich 9 Yong, Jiongmin 8 Achdou, Yves 8 Albano, Paolo 8 Atar, Rami 8 Bokanowski, Olivier 8 Caselles Costa, Vicent 8 Cesaroni, Annalisa 8 Charro, Fernando 8 Galise, Giulio 8 Guillen, Nestor 8 Hamamuki, Nao 8 Hu, Ying 8 Hynd, Ryan 8 Jensen, Robert R. ...and 2,196 more Authors
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#### Cited in 349 Serials

 142 Journal of Differential Equations 113 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 97 Communications in Partial Differential Equations 89 Journal of Mathematical Analysis and Applications 82 Calculus of Variations and Partial Differential Equations 60 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 59 Archive for Rational Mechanics and Analysis 59 Applied Mathematics and Optimization 58 Stochastic Processes and their Applications 54 Journal de Mathématiques Pures et Appliquées. Neuvième Série 53 NoDEA. Nonlinear Differential Equations and Applications 49 Nonlinear Analysis. Theory, Methods & Applications 46 Transactions of the American Mathematical Society 42 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 38 Journal of Functional Analysis 35 Proceedings of the American Mathematical Society 35 SIAM Journal on Control and Optimization 33 Journal of Optimization Theory and Applications 33 The Annals of Applied Probability 33 Discrete and Continuous Dynamical Systems 28 The Annals of Probability 26 Advances in Mathematics 24 Journal of Scientific Computing 22 Communications on Pure and Applied Analysis 21 Journal of Computational Physics 21 Comptes Rendus. Mathématique. Académie des Sciences, Paris 20 Communications on Pure and Applied Mathematics 19 Mathematische Annalen 19 Finance and Stochastics 18 Applicable Analysis 18 Numerische Mathematik 18 Probability Theory and Related Fields 17 Computers & Mathematics with Applications 17 Journal of Computational and Applied Mathematics 17 Journal of Mathematical Sciences (New York) 16 SIAM Journal on Mathematical Analysis 16 Stochastics 15 Automatica 15 Communications in Contemporary Mathematics 14 Systems & Control Letters 14 Applied Numerical Mathematics 13 Mathematics of Computation 13 Stochastic Analysis and Applications 13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 12 Journal of Economic Dynamics & Control 12 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 Potential Analysis 11 Applied Mathematics and Computation 11 Acta Applicandae Mathematicae 10 Queueing Systems 10 Journal of Evolution Equations 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 SIAM Journal on Financial Mathematics 9 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 9 The Journal of Geometric Analysis 9 Nonlinear Analysis. Real World Applications 8 Mathematics of Operations Research 8 Proceedings of the Japan Academy. Series A 8 Dynamic Games and Applications 7 Insurance Mathematics & Economics 7 Chinese Annals of Mathematics. Series B 7 Revista Matemática Iberoamericana 7 Bulletin des Sciences Mathématiques 7 Mathematical Finance 7 Acta Mathematica Sinica. English Series 7 Stochastics and Dynamics 6 Journal of Mathematical Biology 6 Mathematical Methods in the Applied Sciences 6 Annali di Matematica Pura ed Applicata. Serie Quarta 6 Duke Mathematical Journal 6 Journal of Economic Theory 6 Japan Journal of Industrial and Applied Mathematics 6 Journal of Global Optimization 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Journal of Dynamics and Differential Equations 6 SIAM Journal on Scientific Computing 6 International Journal of Theoretical and Applied Finance 6 Interfaces and Free Boundaries 6 Discrete and Continuous Dynamical Systems. Series B 6 Advanced Nonlinear Studies 6 Boundary Value Problems 6 Mathematics and Financial Economics 6 Science China. Mathematics 6 Advances in Nonlinear Analysis 5 Advances in Applied Probability 5 Communications in Mathematical Physics 5 Journal d’Analyse Mathématique 5 Journal of Applied Mathematics and Mechanics 5 Nonlinearity 5 Journal of Mathematical Economics 5 Acta Mathematicae Applicatae Sinica. English Series 5 Annals of Operations Research 5 Journal of Mathematical Imaging and Vision 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Electronic Journal of Probability 5 Abstract and Applied Analysis 5 Revista Matemática Complutense 5 Frontiers of Mathematics in China 5 Discrete and Continuous Dynamical Systems. Series S 5 Advances in Calculus of Variations ...and 249 more Serials
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#### Cited in 51 Fields

 1,621 Partial differential equations (35-XX) 863 Calculus of variations and optimal control; optimization (49-XX) 510 Probability theory and stochastic processes (60-XX) 384 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 348 Systems theory; control (93-XX) 259 Numerical analysis (65-XX) 136 Operations research, mathematical programming (90-XX) 107 Differential geometry (53-XX) 89 Operator theory (47-XX) 73 Ordinary differential equations (34-XX) 66 Integral equations (45-XX) 64 Biology and other natural sciences (92-XX) 56 Dynamical systems and ergodic theory (37-XX) 53 Global analysis, analysis on manifolds (58-XX) 53 Mechanics of particles and systems (70-XX) 47 Computer science (68-XX) 45 Real functions (26-XX) 42 Fluid mechanics (76-XX) 40 Mechanics of deformable solids (74-XX) 33 Statistical mechanics, structure of matter (82-XX) 31 Information and communication theory, circuits (94-XX) 25 Functional analysis (46-XX) 24 Several complex variables and analytic spaces (32-XX) 18 Potential theory (31-XX) 15 Classical thermodynamics, heat transfer (80-XX) 14 Convex and discrete geometry (52-XX) 13 Statistics (62-XX) 11 Optics, electromagnetic theory (78-XX) 8 Measure and integration (28-XX) 8 Difference and functional equations (39-XX) 7 Topological groups, Lie groups (22-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Abstract harmonic analysis (43-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Relativity and gravitational theory (83-XX) 4 General topology (54-XX) 3 Nonassociative rings and algebras (17-XX) 3 Functions of a complex variable (30-XX) 3 Quantum theory (81-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Algebraic geometry (14-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Manifolds and cell complexes (57-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Algebraic topology (55-XX) 1 Mathematics education (97-XX)

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