Rchr

J-GLOBAL ID：200901001928650302 Update date: Dec. 18, 2024

Aikawa Hiroaki

アイカワヒロアキ | Aikawa Hiroaki

Affiliation and department：
Homepage URL (1)： http://www.math.sci.hokudai.ac.jp/~aik

Research field (4)： Mathematical analysis , Geometry , Algebra , Basic analysis

Research keywords (32)： Martin境界 , 調和関数 , ポテンシャル , 放物型方程式 , フラクタル , Dirichlet解 , ソボレフ関数 , 境界Harnack原理 , 容量密度条件 , 一様領域 , 放物型偏微分方程式 , マルチン境界 , 調和 , 楕円型偏微分方程式 , John領域 , Carleson評価 , 漸近挙動 , 熱方程式 , 境界値 , 確率過程 , 容量 , 境界挙動 , 優調和関数 , 境界条件 , 時間遅れをもつ方程式 , ネットワーク , 整関数 , 関数微分方程式 , 極小尖細 , 内部一様領域 , 数学基礎解析学 , Mathematics Analysis

Research theme for competitive and other funds (52)：

2021 - 2026 容量的幅の負曲率多様体への拡張とその応用
2021 - 2024 Study of Analysis and Geometry of complex spaces
2017 - 2022 Analysis of elliptic operators and its applications to Geometric Function Theory
2017 - 2022 Anomalous diffusions on disordered media
2017 - 2021 複雑領域のポテンシャル解析の深化-非線形PDEと理想境界への応用

2016 - 2021 Degeneration and collapsing of Kleinian groups; geometry and analysis of the compactification of their defamation spaces

2017 - 2020 Relation between structure of spaces and analysis

2014 - 2017 Relation between algebra, geometry and analysis on fractals

2013 - 2017 Potential theory on space complexity and ideal boundary

2013 - 2017 Stochastic processes on disordered media -- discrete models and their scaling limits

2013 - 2016 Harnack inequalities with dusts

2010 - 2015 Analysis of degenerations and singularities of Kleinian groups and complex dynamics

2011 - 2014 Interaction between areas of Mathematics related to internal structures of fractals

2010 - 2013 Markov chains on disordered media and their scaling limits

2008 - 2012 Research on potential problems from various aspects

2008 - 2010 Aspects of Mathematics on Fractals

2007 - 2009 非線型方程式の理想境界

2007 - 2008 Potential theoretic study of Sobolev functions

2006 - 2008 Developments of the theory of stochastic processes and real analysis on disordered media

2005 - 2008 Asymptotic analysis of heat kernels and Green functions and its applications

2005 - 2008 Research on deformations of real and complex manifolds and variations of invariants

2005 - 2007 Aspects of Mathematics on Fractals

2004 - 2006 Approach to the qualitative theory of functional equations by phase plane analysis

2003 - 2006 Potential analysis

2003 - 2004 ANALYSIS OF SYSTEMS OF DIFFERENTIAL EQUATIONS HAVING SEVERAL NONLOCAL TERMS AND APPLICATIONS

2001 - 2004 A synthetic study of positive solutions to elliptic and parabolic partial differential equations

2001 - 2004 Integrated Study of Complex Analytic Structure

2001 - 2003 複雑集合の内と外のポテンシャル解析

2001 - 2002 Integrated research of the Theory of infinite networks and their applications

2001 - 2002 System of nonlocal nonlinear differential equations and applications

2000 - 2002 Interdisciplinary research on complicated sets related to functional equations

1999 - 2002 Interdisciplinary research on potential analysis

1999 - 2000 Variational Problems on an infinite network and their applications

1999 - 2000 A versatile study of positive solutions to parabolic and elliptic partial differential equations

1998 - 2000 Applications of analyticoty of functions

1998 - 1999 Theory and Applications of Evolution Equations with Nonlocal Conditions

1998 - 1999 Potential the Oretic study on quasi-regular mappings

1997 - 1998 THEORY OF IDEAL BOUNDARIES OF AN INFINITE NETWORK AND ITS APPLICATION

1997 - 1998 On the research of topological dimension of metric spaces

1997 - 1998 Structure of positive solutions to second order elliptic and parabolic partial differential equations

1997 - 1998 Potential theoretic research on elliptic differential equations

1996 - 1996 積分方程式の解の定性的研究

1996 - 1996 ポテンシャル論の応用

1995 - 1995 ガウス過程の表現と積分方程式

1995 - 1995 ポテンシャル論

1994 - 1994 微分方程式の数式処理システムの研究

1994 - 1994 群論の古典的問題

1994 - 1994 無限可積分系への有限群論からのアプローチ

1992 - 1992 微分方程式の解の構造の研究

1991 - 1991 偏微分方程式に応用のある解析接続の研究

ポテンシャル論

Potential Theory

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Papers (41)：

ｍore...

MISC (5)：

Aikawa Hiroaki. Boundary Harnack principle and the quasihyperbolic boundary condition : Expository and correction (Potential Theory and its related Fields). RIMS Kokyuroku. 2009. 1669. 1-13
Aikawa Hiroaki. BOUNDARY ESTIMATES OF $p$-HARMONIC FUNCTIONS IN A METRIC MEASURE SPACE(Harmonic Analysis and Nonlinear Partial Differential Equations). RIMS Kokyuroku. 2006. 1491. 126-138
Aikawa Hiroaki. FATOU AND LITTLEWOOD THEOREMS FOR POISSON INTEGRALS WITH RESPECT TO NON-INTEGRABLE KERNELS (Harmonic Analysis and Nonlinear Partial Differential Equations). RIMS Kokyuroku. 2004. 1389. 1-11
AIKAWA Hiroaki. Integral representations of weighted Beppo Levi functions(Potential Theory and Its Related Fields). RIMS Kokyuroku. 1987. 610. 1-26
AIKAWA Hiroaki. On the minimal thinness in a Lipschitz domain(POTENTIAL THEORY AND ITS APPLICATIONS). RIMS Kokyuroku. 1983. 502. 13-36

Books (2)：

Norm estimate of the Green operator and its application
In Complex analysis and differential equations(Uppsala, 1997), Uppsala Univ. 1999
Potential Theory : Selected Topics (jointly worked)
Springer Lecture Notes in Mathematics 1996

Education (4)：

- 1980 Hiroshima University
- 1980 Hiroshima University Graduate School, Division of Natural Science
- 1978 Kyoto University Faculty of Science
- 1978 Kyoto University Faculty of Science

Professional career (1)：

(BLANK)

Work history (1)：

2006 - 2012 北海道大学理学(系)研究科(研究院) 教授

Association Membership(s) (2)：

アメリカ数学会(American Mathematical Society) , 日本数学会

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