Rchr
J-GLOBAL ID：201201054730355730
Update date: Feb. 01, 2024
Koike Shigeaki
コイケ シゲアキ | Koike Shigeaki
Affiliation and department：
Homepage URL (2)：
https://www.f.waseda.jp/skoike/index.html
,
https://www.f.waseda.jp/skoike/KoikeE.html
Research field (1)：
Basic analysis
Research keywords (2)：
粘性解理論
, Fully Nonlinear Partial Differential Equations
Research theme for competitive and other funds (44)：
- 1988 - 現在 粘性解理論とその応用
- 2020 - 2025 Regularity theory for viscosity solutions of fully nonlinear equations and its applications
- 2016 - 2021 New development of mathematical theory of turbulence by collaboration of the nonlinear analysis and computational fluid dynamics
- 2016 - 2020 Evolution equations describing non-standard irreversible processes
- 2016 - 2020 New developments of the theory of viscosity solutions and its applications
- 2015 - 2020 Fusion and evolution of asymptotic analysis and geometric analysis in partial differential equations
- 2014 - 2018 Geometric studies on singularity of non-linear phenomena
- 2011 - 2016 Deepening of the theory of viscosity solutions and its applications
- 2011 - 2016 Fundamental theory for viscosity solutions of fully nonlinear equations and its applications
- 2011 - 2016 Geometric properties and asymptotic behavior of solutions of diffusion equations
- 2010 - 2014 A research on the geometric singularities of non-linear phenomena
- 2009 - 2014 Studies on a unified point of view on global theories of nonlinear elliptic equations
- 2010 - 2012 Analysis of gradient flow for the bending energy of plane curves under multiple constraints
- 2009 - 2012 Synthetic study of nonlinear evolution equation and its related topics
- 2008 - 2012 Development of the methods of stochastic control and filtering in mathematical finance
- 2009 - 2011 Stability analysis on solitary wave solutions for systems of nonlinear wave equations
- 2008 - 2010 Viscosity solution theory for fully nonlinear equations and its applications
- 2007 - 2010 Stochastic least principle and its applications
- 2006 - 2009 Differential Geometry and Partial Differential Equations as an application of Singularity theory
- 2006 - 2009 RESEARCH ON THE THEORY OF VISCOSITY SOLUTIONS OF DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS
- 2006 - 2008 An arithmetic study of modular forms of half integral weight and Siegel modular forms
- 2006 - 2008 STUDIES ON STABILITY OF SOLITARY WAVES AND BLOWUP OF SOLUTIONS FORNONLINEAR WAVE EQUATIONS
- 2005 - 2007 Reserch on the stability of solutions of geometric evolution equation using group equivariance
- 2004 - 2007 Expected utility maximiaation problems and stochastic control
- 2004 - 2007 On the study of the theory of viscosity solutions and its new developments
- 2003 - 2006 Geometry of singularities of mapping II
- 2004 - 2005 Arithmetic study of Fourier coefficients of modular forms of half integral weight and Siegel modular forms
- 2003 - 2005 Research on the theory of viscosity solutions and its applications
- 2003 - 2004 Research on geometric evolution equations for hypersurfaoes
- 2001 - 2003 BELLMAN EQUATIONS OF RISK-SENRSITIVE STOCHASTIC AND THEIR APPLICATIONS
- 2000 - 2002 Research on viscosity solutions of differential equations and their applications
- 2000 - 2002 Study on Optimal Controls and Differential Games via the Viscosity Solution Theory
- 2000 - 2002 Optimal Control Theory of Enler-BernouIIi Equation
- 1999 - 2000 On the stracture of solutions of partial differential eauqtions
- 1997 - 1999 Theory and applications of viscosity solutions
- 1997 - 1999 Applications to the optimal control and differential game via the viscosity solution theory
- 1996 - 1997 The study of the pole of the zeta function.
- 1996 - 1996 偏微分方程式の局所および大域解析
- 1995 - 1996 On Birational Geometry of Algebraic Varieties
- 1995 - 1995 Joint Study on Viscosity Solutions and Their Applications
- 1994 - 1994 非線形退化楕円型方程式の粘性解の研究
- 1993 - 1993 特異な境界条件を持った偏微分方程式の最適制御理論
- 1992 - 1992 二階非線形退化楕円型方程式及び方程式系の粘性解の理論と応用
- 1992 - 1992 多様体の大域的構造の研究
Show all
Papers (46)：
MISC (18)：
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KOIKE Shigeaki. On the ABP maximum principle and applications. Advanced Studies in Pure Mathematics. 2015. 64. 113-124
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小池茂昭. 粘性解が古典解になる時 -Caffarelliの研究の紹介-. 数学. 2010. 62. 3. 315-328
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Koike Shigeaki. Weak Harnack inequality for fully nonlinear PDEs with superlinear growth terms in $Du$ (Viscosity Solutions of Differential Equations and Related Topics). RIMS Kokyuroku. 2010. 1695. 139-147
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Koike Shigeaki. Perron-Ishii method for viscosity solutions(Potential Theory and its Related Fields). RIMS Kokyuroku. 2007. 1553. 44-58
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Koike Shigeaki. Maximum principle via the iterated comparison function method(Viscosity Solution Theory of Differential Equations and its Developments). RIMS Kokyuroku. 2007. 1545. 1-12
ｍore...
Books (7)：
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Nonlinear Partial Differential Equations for Future Applications
2021
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粘性解 -比較原理を中心に-
2016
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リメディアル数学
数学書房 2011
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微分積分
数学書房 2010
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International Conference for the 25th Anniversary of Viscosity Solutions
学校図書 2008
ｍore...
Lectures and oral presentations (22)：
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ABP maximum principle with upper contact sets for fully nonlinear elliptic PDEs
(OIST PDE seminar 2022)
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Lp viscosity solution theory -revisited-
(The 20th Northeastern Symposium on Mathematical Analysis 2019)
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Obstacle problems for PDE of non-divergence type
(研究集会「第14回 非線型の諸問題」 2018)
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Recent development on Lp viscosity solutions for fully nonlinear parabolic PDE
(九州における偏微分方程式研究集会 2018)
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自由境界問題の近似問題
(室蘭非線形解析研究会 2017)
ｍore...
Education (2)：
- - 1988 Waseda University Graduate School, Division of Science and Engineering
- - 1981 Waseda University Faculty of Science and Engineering 物理学科
Professional career (1)：
- 理学(数学) (Waseda University)
Work history (6)：
Committee career (4)：
- 2022/04 - 2023/03 日本数学会 評議員
- 2016/05 - 2016/10 函数方程式論分科会 解析学賞選考委員
- 2013/05 - 2013/10 函数方程式論分科会 解析学賞選考委員
- 2012/05 - 2012/10 函数方程式論分科会 解析学賞選考委員長
Awards (2)：
- 2016/09 - 日本数学会 解析学賞 完全非線形楕円型・放物型偏微分方程式のLp粘性解理論
- 2010/03 - 日本数学会 JMSJ Outstanding Paper Prize
Association Membership(s) (1)：
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