KOIKE Shigeaki

J-GLOBAL         Last updated: Jul 22, 2019 at 16:25
KOIKE Shigeaki
Waseda University
Faculty of Science and Engineering
理学(数学)(Waseda University)

Research Areas


Academic & Professional Experience

Professor, Tohoku University Graduate School of Science Mathematics Analysis
Apr 2012
教授, 東北大学
Apr 2006
Mar 2012
教授, 埼玉大学大学院理工学研究科
Apr 1992
Mar 2002
助教授, 埼玉大学理学部
Oct 1989
Mar 1992
助手, 東京都立大学理学部


Mar 1988
Graduate School, Division of Science and Engineering, Waseda University
Mar 1981
物理学科, Faculty of Science and Engineering, Waseda University

Committee Memberships

May 2013
Oct 2013
函数方程式論分科会  解析学賞選考委員
May 2012
Oct 2012
函数方程式論分科会  解析学賞選考委員長

Awards & Honors

Sep 2016
完全非線形楕円型・放物型偏微分方程式のLp粘性解理論, 解析学賞, 日本数学会
Mar 2010
JMSJ Outstanding Paper Prize, 日本数学会
Winner: 小池茂昭, Andrzej Swiech

Published Papers

S. Koike, T. Kosugi and M. Naito
Journal of Mathematical Analysis and Applications   457(1) 436-460   Jan 2018   [Refereed]
S. Koike and T. Kosugi
Nonlinear Analysis   160 1-15   Sep 2017   [Refereed]
Remarks on mean curvature flow with obstacles
K. Ishii, H. Kamata and S. Koike
Mathematics for Nonlinear Phenomena: Analysis and Computation, Proceedings in Mathematics and Computation   215 83-103   Jul 2017   [Refereed]
G. Galise, S. Koike, O. Ley and A. Vitolo
Journal of Mathematical Analysis and Applications   441(1) 194-210   2016   [Refereed]
On the ABP maximum principle for Lp-viscosity solutions of fully nonlinear PDE
S. Koike
Nonlinear Dynamics in Partial Differential Equations, Advanced Studies in Pure Mathematics   64 113-124   2015   [Refereed]
G. Barles, S. Koike, O. Ley and E. Topp
Calculus of Variations and Partial Differential Equations   54(1) 539-572   2015   [Refereed]
S. Koike and T. Kosugi
Communications in Pure and Applied Analysis   14(1) 133-142   2015   [Refereed]
On the ABP maximum principle and applications
S. Koike
RIMS Kokyuroku   1845 107-120   2013
S. Koike and A. Swiech
Indiana Universiy Mahemaical Journal   62(5) 1473-1502   2013   [Refereed]
S. Koike and A. Swiech
Communications in Pure and Applied Analysis   11(5) 1897-1910   Sep 2012   [Refereed]
S. Koike and O. Ley
Journal of Mathematical Analysis and Applications   381(1) 110-120   Sep 2011   [Refereed]
Recent developments on maximum principle for Lp-viscosity solutions of fully nonlinear elliptic/parabolic PDEs
S. Koike
Recent Progress on Reaction-diffusion Systems and Viscosity Solutions   131-153   2009   [Refereed]
S. Koike and A. Swiech
Journal of Mathematical Society of Japan   61(3) 723-755   2009   [Refereed]
S. Koike and A. Swiech
Journal of the Fixed Point Theory and its Applications   5(2) 291-304   2009   [Refereed]
Remarks on the Phragmén-Lindelöf Theorem for Lp-viscosity solutions of fully nonlinear PDEs with unbounded ingredients
S. Koike and K. Nakagawa
Electronic Journal of Differential Equations   2009(146) 1-14   2009   [Refereed]
A linear-quadratic control problem with discretionary stopping
S. Koike, H. Morimoto and S. Sakaguchi
Discrete and Continuous Synamical Systems, series B   8(2) 261-277   2007   [Refereed]
S. Koike and A. Swiech
Mathematische Annalen   339(2) 461-484   2007   [Refereed]
S. Koike and H. Morimoto
Funkcialaj Ekvacioj   48(2) 183-202   2005   [Refereed]
Perron's method for Lp-viscosity solutions
S. Koike
Saitama Mathematical Journal   23 9-28   2005   [Refereed]
S. Koike and A. Swiech
Nonlinear Differential Equations and Applications   11(4) 491-509   2004   [Refereed]
S. Koike and H. Morimoto
Applied Mathematics and Optimizations   48(1) 1-20   2003   [Refereed]
Remarks on regularity of viscosity solutions for fully nonlinear uniformly elliptic PDEs with measurable ingredients
S. Koike and T. Takahashi
Advances in Differential Equations   7(4) 493-512   2002   [Refereed]
On fully nonlinear PDEs derived from variational problems Lp norms
T. Ishibashi and S. Koike
SIAM Journal on Mathematical Analysis   33(3) 545-569   2002   [Refereed]
On the pursuit-evasion game with state constraint
M. Bardi, S. Koike and P. Soravia
Discrete and Continuous Dynamical Systems   6(2) 361-380   2000   [Refereed]
O. Alvarez, S. Koike and I. Nakayama
SIAM Journal on Control and Optimization   38(2) 470-481   2000   [Refereed]
On ε-optimal controls for state constraint problem
H. Ishii and S. Koike
Annales de l'Institut Henri Poincaré, Analyse Non linéaire   17(4) 473-502   2000   [Refereed]
A comparison result for the state constraint problem of differential games
S. Koike
Proceedings of Korean-Japan Partial Differential Equations Conference   1-8   1997
Semicontinuous viscosity solutions for Hamilton-Jacobi equations with a degenerate coefficient
S. Koike
Differential and Integral Equations   10(3) 455-472   1997   [Refereed]
H. Ishii and S. Koike
SIAM Journal, Control and Optimization   34(2) 554-571   1996   [Refereed]
On the Bellman equations with varying control
S. Koike
Bulletin of the Australian Mathematical Society   53(1) 51-62   1996   [Refereed]
The state constraint problem for differential games
S. Koike
Indiana University Mathematics Journal   44(2) 467-487   1995   [Refereed]
Uniqueness of viscosity solutions for monotone systems of fully nonlinear PDEs under Dirichlet condition
S. Koike
Nonlinear Analysis, Theory, Methods and Applications   22(4) 519-532   1994   [Refereed]
Viscosity solutions of monotone systems for Dirichlet problems
M. Katsoulakis and S. Koike
Differential and Integral Equations   7(2) 367-382   1994   [Refereed]
A viscosity solution approach to functional differential equations
S. Koike
Proceedings of the Second GARC SYMPOSIUM on Pure and Applied Mathematics   17 213-219   1993
Viscosity solutions of functional differential equations
H. Ishii and S. Koike
Advances in Mathematical Sciences and Applications   3 191-218   1993   [Refereed]
H. Ishii and S. Koike
Applied Mathematics and Optimization   23(1) 1-17   1991   [Refereed]
On the rate of convergence of solutions in singular perturbation problems
S. Koike
Journal of Mathematical Analysis and Applications   157(1) 243-253   1991   [Refereed]
Viscosity solutions of a system of nonlinear second-order elliptic PDEs arising in switching games
H. Ishii and S. Koike
Funkcialaj Ekvacioj   34(1) 143-155   1991   [Refereed]
Viscosity solutions for monotone systems of second-order elliptic PDEs
H. Ishii and S. Koike
Communications in Partial Differential Equations   16(6-7) 1095-1128   1991   [Refereed]
An asymptotic formula for solutions of Hamilton-Jacobi-Bellman equations
S. Koike
Nonlinear Analysis, Theory, Methods and Applications   11(3) 429-436   1987   [Refereed]
On the regularity of solutions of a degenerate parabolic Bellman equation
S. Koike
Hiroshima Mathematical Journal   16(2) 251-267   1986   [Refereed]
Boundary regularity and uniqueness for an elliptic equation with gradient constraint
H. Ishii and S. Koike
Communications in Partial Differential Equations   8(4) 317-346   1983   [Refereed]


粘性解が古典解になる時 -Caffarelliの研究の紹介-
数学   62(3) 315-328   Oct 2010
49(1) 2-7   2005
小池茂昭, 山田直記
数学   47 20-28   1995

Books etc

泉屋周一他 (Part:Joint Work, 1章)
数学書房   2011   
数学書房   2010   
International Conference for the 25th Anniversary of Viscosity Solutions
Yoshikazu Giga 他 (Part:Joint Editor)
学校図書   2008   
小薗英雄他 (Part:Joint Work, 151~168)
日本評論社   May 2007   
A Beginner's Guide to the Theory of Viscosity Solutions
Shigeaki Koike
Mathematical Society of Japan   2007   

Conference Activities & Talks

On the rate of convergence in free boundary problems [Invited]
The 5th Italian-Japanese Workshop on Geometrc Properties for Parabolic and Elliptic PDE's   15 May 2017   
Fully nonlinear uniformly elliptic/parabolic PDE with unbounded ingredients
Hamilton-Jacobi Equations New trends and applications   30 May 2016   
Entire solutions of fully nonlinear elliptic PDE with super linear gradient terms [Invited]
Workshop on nonlinear partial differential equations and related topics   9 May 2016   
ABP最大値原理について [Invited]
日本数学会2016年度年会   16 Mar 2016   
Holder continuity for subsolutions of integer-differential equations
偏微分方程式の漸近問題と粘性解   2 Dec 2015   

Association Memberships


Research Grants & Projects

Project Year: Apr 1988 - Today

Social Contribution

[Others]  17 Aug 2014 - 19 Aug 2014
[Others]  5 Dec 2013


Apr 2010   粘性解の基礎理論の新展開
Apr 2008   完全非線形方程式の粘性解の基礎理論
Apr 2007   粘性解理論とその先端的応用
Apr 2007   粘性解生誕25周年国際研究集会
Apr 2006   粘性解の微分可能性と最適制御に関する基礎研究