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J-GLOBAL ID：200901097628940268   Update date: Apr. 17, 2024

Horiuchi Toshio

ホリウチ トシオ | Horiuchi Toshio
Affiliation and department：
Ibaraki University Graduate School of Science and Engineering (Science), Department of Science (Mathematics and Informatics Course)

About Ibaraki University Graduate School of Science and Engineering (Science), Department of Science (Mathematics and Informatics Course)


Job title： Professor
Homepage URL  (1)： http://www.sci.ibaraki.ac.jp
Research field  (3)： Basic analysis ,  Basic analysis ,  Basic analysis
Research keywords  (16)： weighted Sobolev inewualities ,  退化楕円型方程式 ,  非線形楕円型方程式 ,  variational analysis ,  Removable singularities to solutions of nonlinear elliptic equations with absorption term ,  Minimal solutions to quasi-inear elliptic equations ,  p-capacity, p-Laplace-capacity, Hausdorff measure ,  ハーディー・ソボレフ・レリッヒ型不等式 ,  improved nonlinear Kato's inequalities ,  improved Kato's inequalities and nonlinear obstacle problems ,  Kato's inequalities up to boundary ,  Inverse Maximum Principle ,  Nonlinear Storong maximum prinviple ,  Critical Caffarelli-Kohn-Nirenberg type inequalities ,  古典的不等式のミッシングターム ,  Caffarelli-Kohn-Nirenberg type inequalities
Research theme for competitive and other funds  (26)：
  • 2016 - 2020 古典的不等式の精密化に基づく非線型楕円型方程式の定性的研究
  • 2015 - 2020 実解析・調和解析に由来する関数空間の理論の深化と応用
  • 2013 - 2016 熱方程式・波動方程式の解を保つ変換の研究
  • 2012 - 2016 古典的不等式の精密化とその楕円型変分問題への応用
  • 2012 - 2015 変動する指標をもつ関数空間を基礎とした調和解析とその応用
Show all
Papers (37)：
  • Toshio Horiuchi. On the Caffarelli-Kohn-Niremberg type inequalities and related topics [translation]. Sugaku Expositions. 2019. 32. 2. 233-259
  • Xiaojing Liu, Toshio Horiuchi. Kato’s inequalities for admissible functions to quasilinear elliptic operators A. Mathematical Journal of Ibaraki University. 2019. 51. 49-64
  • Toshio Horiuchi, Xiaojing Liu. The equivalences among p-capacity, p-Laplace-capacities and Hausdorff measure. Mathematical Journal of Ibaraki University. 2018. 50. 5-13
  • Xiaojing Liu, Toshio Horiuchi. Remarks on the strong maximum principle involving p-Laplacian. HIROSHIMA MATHEMATICAL JOURNAL. 2016. 46. 3. 311-331
  • Remarks on Kato’s inequality when Δp u is a measure,. Mathematical Journal of Ibaraki University. 2016. 48. 45-61
ｍore...
MISC (20)：
  • Hiroshi Ando, Toshio Horiuchi, Xiaojing Liu. One dimensional weighted Hardy’s inequalities and application. arXiv:1909.10689 [math.AP]; Accepted by Journal of Mathematical Inequalities. 2020. 1-16
  • Toshio Horiuchi, Peter Kumlin. Kato's inequalities up to the boundary for a quasilinear operator. Scientiae Mathematicae Japonicae in Editione Electronica ), e-2019, 32 ;2019-13. 2019. 1-14
  • Horiuchi Toshio, Peter Kumlin. Erratum to: "On the minimal solution for quasilinear degenerate elliptic equation and its blow-up" [J. Math. Kyoto Univ. J. Math. Kyoto Univ. 2006. 46. 1
  • Alnar. Detalla, Toshio. Horiuchi, Hiroshi. Ando. Sharp remainder terms of Hardy- Sobolev inequalities. Math. J. Ibaraki Univ. 2005. 37. 39--52-52
  • T Horiuchi, P Kunlin. On the minimal solution for quasilinear degenerate elliptic equation and its blow-up. JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY. 2004. 44. 2. 381-439
ｍore...
Books (5)：
  • 線形代数、微積分から関数解析へ(数理科学)
    サイエンス社 2017
  • Caffarelli-Kohn-Nirenberg 型不等式とその周辺 (数学)
    日本数学会 2016
  • 関数解析の基礎
    内田老鶴圃 2005 ISBN:4753600998
  • 複素解析の基礎
    内田老鶴圃 2001
  • Foundation of modern analysis
    Uchida Roukukuho 1989
Lectures and oral presentations  (87)：
  • One dimensional weighted Hardy's inequalities and application
    (Meeting of Mathematical society of Japan 2019)
  • One dimensional Weighted Hardy’s Inequalities and application
    (調和解析セミナー 2019)
  • Weighted Hardy's inequalities with compact perturbations.
    (調和解析セミナー 2019)
  • On Kato's inequalities and relating topics
    (International congress of Mathematician, 2018 (ICM 2018 Rio) 2018)
  • The equivalences among p-capacity, p-Laplace-capacites and Hausdorff measure
    (日本数学会 函数方程式分科会 2018)
ｍore...
Professional career (1)：
  • 理学博士 (京都大学)
Work history (3)：
  • 1995/04 - Professor; Ibaraki University Faculty of Science Department of Mathematical Sciences
  • 1988/04 - 1995/03 Assistant Professor ; Ibaraki University Faculty of Science Department of Mathematics
  • 1982/04 - 1988/03 Assistant; Ibaraki University Faculty of Science Department of Mathematics
Committee career (1)：
  • 1999/04 - 2001/03 日本数学会 評議員
Association Membership(s) (1)：
日本数学会
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