MIYAZAKI Yoichi

School of Dentistry Department of DentistryProject Professor

Researcher Information

Research Keyword

  • heat kernel
  • Lp theory
  • spectral function
  • elliptic operator
  • Basic Analysis

Field Of Study

  • Natural sciences, Basic analysis, Basic Analysis

Career

  • Apr. 1996 - Present
    千葉大学 非常勤講師
  • Oct. 2016 - Mar. 2023
    日本大学 教授
  • Oct. 2013 - Sep. 2016
    日本大学 准教授
  • Oct. 2013 - Mar. 2014
    東京理科大学 非常勤講師
  • Nov. 2005 - Sep. 2013
    日本大学 専任講師
  • Apr. 1996 - Oct. 2005
    日本大学 講師（専任扱）
  • Oct. 1988 - Mar. 1996
    日本大学 助手

Educational Background

  • 1981
    The University of Tokyo, Faculty of Science, Department of Mathematics
Research activity information

Award

  • 私立大学情報教育協会賞

Paper

  • Tartar's method for the Riesz-Thorin interpolation theorem
    Yoichi Miyazaki
    Archiv der Mathematik, Sep. 2021, Refereed, Not invited
    Lead
  • A short proof of the Gagliardo-Nirenberg inequality with BMO term
    Yoichi Miyazaki
    Proceedings of the American Mathematical Society, May 2020, Refereed, Not invited
    Lead
  • Sobolev inequalities via Muramatu's integral formula
    Yoichi Miyazaki
    Le Matematiche, Nov. 2019, Refereed, Not invited
    Lead
  • Poisson's integral formula via heat kernels
    Yoichi Miyazaki
    Analysis - International mathematical journal of analysis and its applications, Aug. 2019, Refereed, Not invited
    Lead
  • Lp regularity theorem for elliptic equations in less smooth domains
    Yoichi Miyazaki
    Journal of Mathematical Society of Japan, Jul. 2019, Refereed, Not invited
    Lead
  • Introduction to L (p) Sobolev Spaces via Muramatu's Integral Formula
    Yoichi Miyazaki
    MILAN JOURNAL OF MATHEMATICS, Jun. 2017, Refereed, Not invited
  • Sobolev trace theorem and the Dirichlet problem in a ball
    Miyazaki Y
    Int. Journal of Math. Analysis, Dec. 2016, Refereed, Not invited
    Lead
  • Boundary behavior of Dirichlet eigenfunctions for a ball
    Miyazaki Y
    Transactions of Nihon University School of Dentistry, Dec. 2016, Not refereed, Not invited
    Lead
  • 同時性と汎用性に優れたOSCEタイマーの開発
    山崎洋介、宮崎洋一、山岡大、江島堅一郎、磯川桂太郎
    日本歯科医学教育学会雑誌, Aug. 2015, Refereed, Not invited
  • Liouville's theorem and heat kernels
    Yoichi Miyazaki
    EXPOSITIONES MATHEMATICAE, 2015, Refereed, Not invited
  • Sobolev Trace Theorem and the Dirichlet Problem in the Unit Disk
    Yoichi Miyazaki
    MILAN JOURNAL OF MATHEMATICS, Dec. 2014, Refereed, Not invited
  • Another method to evaluate green functions for elliptic equations
    Yoichi Miyazaki
    International Journal of Mathematical Analysis, 2014, Refereed, Not invited
  • Schauder theory for Dirichlet elliptic operators in divergence form
    Yoichi Miyazaki
    Journal of Evolution Equations, Jun. 2013, Refereed, Not invited
  • Asymptotic behavior of normal derivatives of eigenfunctions for the Dirichlet Laplacian
    Yoichi Miyazaki
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Apr. 2012, Refereed, Not invited
  • Norm estimates and integral kernel estimates for bounded operators in Sobolev spaces
    Yoichi Miyazaki
    Proc. Japan Acad., Ser. A, Dec. 2011, Refereed, Not invited
    Lead
  • Heat asymptotics for Dirichlet elliptic operators with non-smooth coefficients
    Yoichi Miyazaki
    ASYMPTOTIC ANALYSIS, May 2011, Refereed, Not invited
  • Kernel estimates for pseudo-differential operators of negative order II
    Miyazaki Y
    Transactions of Nihon University School of Dentistry, Dec. 2010, Not refereed, Not invited
    Lead
  • Differentiability of exponential functions via the limit of a sequence
    Far East Journal of Mathematical Education, Feb. 2010, Refereed, Not invited
    Lead
  • Kernel estimates for pseudo-differential operators of negative order
    Miyazaki Y
    Transactions of Nihon University School of Dentistry, Dec. 2009, Not refereed, Not invited
    Lead
  • 書評: 宮島静雄:ソボレフ空間の基礎と応用, 共立出版, 2006年, v$+$309ページ
    宮崎 洋一
    数学, Oct. 2009, Refereed, Not invited
    Lead
  • Spectral asymptotics for Dirichlet elliptic operators with non-smooth coefficients
    Yoichi Miyazaki
    Osaka Journal of Mathematics, Jun. 2009, Refereed, Not invited
    Lead
  • New proofs of the trace theorem of Sobolev spaces
    Yoichi Miyazaki
    Proc. Japan Acad., Ser. A, Jul. 2008, Refereed, Not invited
    Lead
  • Corrigendum to "Higher order elliptic operators of divergence form in C1 or Lipschitz domains" [J. Differential Equations 230 (2006) 174-195] (DOI:10.1016/j.jde.2006.07.024)
    Yoichi Miyazaki
    Journal of Differential Equations, May 2008, Refereed, Not invited
  • Higher order elliptic operators of divergence form in C-1 or Lipschitz domains
    Yoichi Miyazaki
    JOURNAL OF DIFFERENTIAL EQUATIONS, Nov. 2006, Refereed, Not invited
  • The L^p resolvents for elliptic systems of divergence form
    Yoichi Miyazaki
    Advanced Studies in Pure Mathematics, Aug. 2006, Refereed, Not invited
    Lead
  • Simple proof of asymptotic formula for spectral functions of elliptic operators
    Proceedings of the International Conference on Pseudo-differential Operators, Spectral and Scattering Theory and Wavelets --- In Memory of Michihiro Nagase --- (2005/06/29-07/01), Jan. 2006, Not refereed, Not invited
    Lead
  • Setting up the internet server
    宮崎洋一; 磯川桂太郎; 網干博文; 江島堅一郎; 大山哲生; 山崎洋介
    Trans Nihon Univ Sch Dent, Dec. 2005, Not refereed, Not invited
  • The L-P theory of divergence form elliptic operators under the Dirichlet condition
    Y Miyazaki
    JOURNAL OF DIFFERENTIAL EQUATIONS, Aug. 2005, Refereed, Not invited
  • L^p theory of divergence form elliptic operators under the Dirichlet boundary condition
    Y Miyazaki
    Proceedings of the 5th East Asia PDE Conference GAKUTO Internat. Ser. Math. Sci. Appl Gakkotosho, Tokyo, 2005, Refereed, Not invited
    Lead
  • Dirichlet problem for ordinary differential operators and the Laplacian
    Miyazaki Y
    Transactions of Nihon University School of Dentistry, Dec. 2004, Not refereed, Not invited
    Lead
  • Perlの活用によるネットワークでのデータ収集
    宮崎洋一; 磯川桂太郎; 田辺直紀; 向山レイ
    Transactions of Nihon Universit School of Dentistry, Dec. 2004, Not refereed, Not invited
    Lead
  • The L-P resolvents of second-order elliptic operators of divergence form under the Dirichlet condition
    Y Miyazaki
    JOURNAL OF DIFFERENTIAL EQUATIONS, Nov. 2004, Refereed, Not invited
  • Asymptotic behavior of spectral functions for elliptic operators with non-smooth coefficients
    Y Miyazaki
    JOURNAL OF FUNCTIONAL ANALYSIS, Sep. 2004, Refereed, Not invited
  • The Lp resolvents of elliptic operators with uniformly continuous coefficients
    Yoichi Miyazaki
    Journal of Differential Equations, Mar. 2003, Refereed, Not invited
  • Behavior of the spectral function for the biharmonic operator near the boundary
    Miyazaki Y
    Transactions of Nihon University School of Dentistry, 2003, Not refereed, Not invited
    Lead
  • Tauberian theorem by Avakumovic
    Miyazaki Y
    Transactions of Nihon University School of Dentistry (General Studies), 2002, Not refereed, Not invited
    Lead
  • Texによる定型文書の作成
    宮崎洋一; 磯川桂太郎
    日本大学歯学部（一般教育）研究紀要, 2002, Not refereed, Not invited
    Lead
  • CD-ROM化画像教材とWebシステムの連携による組織学教育
    磯川桂太郎; 宮崎洋一
    情報教育方法研究, 2002, Not refereed, Not invited
  • The L^2-boundedness of pseudodifferential operators with simple symbols
    Miyazaki Y
    Funkcial. Ekvac, 2002, Refereed, Not invited
    Lead
  • Behavior of the spectral function for the Laplacian near the boundary
    Miyazaki Y
    Transactions of Nihon University School of Dentistry (General Studies), 2001, Not refereed, Not invited
    Lead
  • Boundedness of pseudodifferential operators with double symbols
    Miyazaki Y
    Transactions of Nihon University School of Dentistry (General Studies), 2000, Not refereed, Not invited
    Lead
  • 書評: Safarov, D. Vassiliev: The Asymptotic Distribution of Eigenvalues of Partial Differential Operators, Translations of Mathematical Monographs, Vol. 155, American Mathematical Society, 354ページ
    数学, Oct. 1999, Refereed, Not invited
    Lead
  • Boundedness of pseudodifferential operators with simple symbols
    Miyazaki Y
    Transactions of Nihon University School of Dentistry (General Studies), 1999, Not refereed, Not invited
    Lead
  • Sobolev空間についてIII
    宮崎洋一
    日本大学歯学部（一般教育）研究紀要, 1998, Not refereed, Not invited
    Lead
  • Asymptotic behavior of spectral functions of elliptic operators with Holder continuous coefficients
    Yoichi Miyazaki; Yoichi Miyazaki
    Journal of the Mathematical Society of Japan, 1997, Refereed, Not invited
  • Sobolev空間についてII
    宮崎洋一
    日本大学歯学部（一般教育）研究紀要, 1997, Not refereed, Not invited
    Lead
  • Sobolev空間についてI
    宮崎洋一
    日本大学歯学部(一般教育)研究紀要, 1996, Not refereed, Not invited
    Lead
  • The eigenvalue distribution of elliptic operators with Ho"lder continuous coefficients
    Miyazaki Y
    Proceedings of the Fourth International Colloquium on Differential Equations, 1994, Refereed, Not invited
    Lead
  • The eigenvalue distribution of elliptic operators with Ho"lder continuous coefficients II
    Miyazaki Y
    Osaka Journal of Mathematics, 1993, Refereed, Not invited
    Lead
  • Remarks on irregular open sets and its application to the eigenvalue distribution
    Miyazaki Y
    Funkcial. Ekvac., 1992, Refereed, Not invited
    Lead
  • Domains of square roots of regularly accretive operators
    Miyazaki Y
    Proceedings of the Japan Academy, Feb. 1991, Refereed, Not invited
    Lead
  • The eigenvalue distribution of elliptic operators with Ho"lder continuous coefficients
    Miyazaki Y
    Osaka Journal of Mathematics, 1991, Refereed, Not invited
    Lead
  • Application of interpolation spaces with a function parameter to the eigenvalue distribution of compact operators
    Miyazaki Y
    Journal of the Faculty of Science, University of Tokyo. Sect. IA., 1991, Refereed, Not invited
    Lead
  • On the asymptotic remainder estimate for the eigenvalues of operators associated with strongly elliptic sesquilinear forms
    Miyazaki Y
    Proceedings of the Japan Academy, 1991, Refereed, Not invited
    Lead
  • The eigenvalue distribution for a degenerate elliptic operator -div((1-|x|^2) grad・)
    Miyazaki Y
    Israel Journal of Mathematics, Feb. 1990, Refereed, Not invited
    Lead
  • A sharp asymptotic remainder estimate for the eigenvalues of operators associated with strongly elliptic sesquilinear forms
    Miyazaki Y
    Japanese Journal of Mathematics, 1989, Refereed, Not invited
    Lead

Lectures, oral presentations, etc.

  • Improvement of the logarithmic Sobolev inequalities with BMO norm
    宮崎洋一
    日本数学会2022年度秋季総合分科会 実函数論分科会, Sep. 2022, 日本数学会, Not invited
  • A tour of Sobolev spaces by Muramatu's integral formula
    Yoichi Miyazaki
    Asia-Pacific Analysis and PDEs Seminar, Oct. 2021, Daniel Hawer (The University of Sydney), Invited
  • A proof of the Gagliardo-Nirenberg inequality with BMO term via Muramatu's integral formula
    宮崎洋一
    日本数学会2020年度秋季総合分科会 実函数論分科会, Sep. 2020, 日本数学会, Not invited
  • Gagliardo-Nirenberg inequality and Muramatu's integral formula
    宮崎洋一
    日本数学会2019年度秋季総合分科会 実函数論分科会, Sep. 2019, Not invited
  • H\"older regularity theorem for elliptic equations in a non-smooth domain
    Yoichi Miyazaki
    The 39th Sapporo Symposium on Partial Differential Equations, Aug. 2014, Not invited
  • Development of an OSCE timer with accurate time synchronization
    山岡大; 山崎洋介; 江島堅一郎; 宮崎洋一; 磯川桂太郎
    第33回 日本歯科医学教育学会学術大会, Jul. 2014, Not invited
  • The regularity theorem for elliptic equations and the smoothness of domains
    宮崎洋一
    東京大学大学院数理科学研究科 解析学火曜セミナー, May 2014, Invited
  • Introduction to complex interpolation between Sobolev spaces
    宮崎洋一
    日本数学会2014年度年会 実函数論分科会, Mar. 2014, Not invited
  • Development of an OSCE timer running on web browsers
    宮崎洋一; 山岡大; 江島堅一郎; 山崎洋介; 磯川桂太郎
    第32回 日本歯科医学教育学会学術大会, Jul. 2013, Not invited
  • 楕円型方程式のLp正則性定理と領域の滑らかさ
    宮崎洋一
    日本数学会2013年度年会 函数方程式論分科会, Mar. 2013, Not invited
  • 楕円型作用素のレゾルベント核の評価法
    宮崎洋一
    日本数学会2012年度秋季総合分科会 実函数論分科会, Sep. 2012, Not invited
  • 発散形楕円型作用素のシャウダー理論
    宮崎洋一
    日本数学会2011年度秋季総合分科会 函数方程式論分科会, Sep. 2011, Not invited
  • ラプラシアンの固有関数の境界での漸近挙動II
    宮崎洋一
    日本数学会2010年度秋季総合分科会 函数方程式論分科会, Sep. 2010, Not invited
  • ラプラシアンの固有関数の境界での漸近挙動
    宮崎洋一
    日本数学会2009年度秋季総合分科会 函数方程式論分科会, Sep. 2009, Not invited
  • ソボレフ空間のトレース定理の簡単な証明
    宮崎洋一
    日本数学会2007年度秋季総合分科会 函数方程式論分科会, Sep. 2007, Not invited
  • Spectral and heat asymptotics for elliptic operators with H\"older continuous coefficients
    Yoichi Miyazaki
    International Congress of mathematicians Madrid 2006, Aug. 2006, Not invited
  • $C^1$領域における発散形の高階楕円型作用素
    宮崎洋一
    日本数学会2006年度年会 函数方程式論分科会, Mar. 2006, Not invited
  • 滑らかでない係数に対する熱核とそのトレースの漸近挙動
    宮崎 洋一
    日本数学会2005年度秋季総合分科会 函数方程式論分科会, Sep. 2005, Not invited
  • L^p theory of divergence form elliptic operators under the Dirichlet condition
    Y Miyazaki
    The 5th East Asia PDE Conference, Feb. 2005, Not invited
  • 発散形楕円型作用素のL^p理論
    日本数学会2004年度秋季総合分科会 函数方程式論分科会, Sep. 2004, Not invited
  • The $L^p$ resolvents for elliptic systems of divergence form
    International Workshop on Potential Theory in Matsue 2004, Aug. 2004, Not invited
  • 発散形の一様連続係数2階楕円型作用素の半空間におけるL^pレゾルベント
    宮崎洋一
    日本数学会2003年度秋季総合分科会 函数方程式論分科会, Sep. 2003, Not invited
  • ヘルダー連続な係数の楕円形作用素に対する熱核の漸近挙動
    宮崎洋一
    日本数学会2001年度秋季総合分科会 函数方程式論分科会, Oct. 2001, Not invited
  • A multicast-aided realtime image delivery and vocally-interactive system complementary to the modernn Web-based learning in histology laboratory
    Keitaro Isokawa
    Experimental Biology, 2001, Not invited
  • 擬微分作用素のL^2有界性
    日本数学会2000年度秋季総合分科会 函数方程式論分科会, Sep. 2000, Not invited
  • 滑らかでない係数の楕円型作用素に対する熱核およびレゾルベント核の微分可能性
    日本数学会1998年度秋季総合分科会 函数方程式論分科会, Oct. 1998, Not invited
  • 双一次形式で定義される作用素の熱核の滑らかさ
    応用数学冬季研究集会98(北大), Feb. 1998, Not invited
  • ヘルダー連続な係数をもつ楕円型作用素のスペクトル関数の漸近挙動
    日本数学会1996年度秋季総合分科会 函数方程式論分科会, Sep. 1996, Not invited
  • The eigenvalue distribution of elliptic operators with Ho"lder continuous coefficients
    The Fourth International Colloquium on Differential Equation, Aug. 1993, Not invited

Affiliated academic society

  • 日本数学会
  • The Mathematical Association of America

Research Themes

  • Theory and application of elliptic operators in divergence form
    2011 - 2015