MEGUMI SANO

Last Updated :2024/02/01

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Associate Professor
E-mail
smegumihiroshima-u.ac.jp

Basic Information

Major Professional Backgrounds

  • 2018/04/01, 2019/03/31, Tokyo Institute of Technology, Department of Mathematics, Research Fellowship for Young Scientists PD
  • 2016/04/01, 2018/03/31, Osaka City University, Department of Mathematics, Research Fellowship for Young Scientists DC2

Academic Degrees

  • Osaka City University
  • Osaka City University

Educational Activity

  • [Bachelor Degree Program] School of Engineering : Cluster 2(Electrical, Electronic and Systems Engineering) : Program of Electrical,Systems and Information Engineering
  • [Master's Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Electrical, Systems, and Control Engineering Program
  • [Master's Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Smart Innovation Program
  • [Doctoral Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Electrical, Systems, and Control Engineering Program
  • [Doctoral Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Smart Innovation Program

Research Fields

  • Mathematical and physical sciences;Mathematics;Mathematical analysis

Research Keywords

  • Variational problem, Hardy's inequality, optimal constant, Nonlinear partial differential equation, non-compactness

Affiliated Academic Societies

Educational Activity

Course in Charge

  1. 2023, Liberal Arts Education Program1, 2Term, Seminar in Basic Mathematics I
  2. 2023, Liberal Arts Education Program1, 4Term, Seminar in Basic Mathematics II
  3. 2023, Undergraduate Education, 1Term, Applied Mathematics II
  4. 2023, Graduate Education (Master's Program) , 1Term, Special Exercises on Electrical, Systems, and Control Engineering A
  5. 2023, Graduate Education (Master's Program) , 2Term, Special Exercises on Electrical, Systems, and Control Engineering A
  6. 2023, Graduate Education (Master's Program) , 3Term, Special Exercises on Electrical, Systems, and Control Engineering B
  7. 2023, Graduate Education (Master's Program) , 4Term, Special Exercises on Electrical, Systems, and Control Engineering B
  8. 2023, Graduate Education (Master's Program) , Academic Year, Special Study on Electrical, Systems, and Control Engineering
  9. 2023, Graduate Education (Master's Program) , 2Term, Mathematics A
  10. 2023, Graduate Education (Doctoral Program) , Academic Year, Special Study on Electrical, Systems, and Control Engineering

Research Activities

Academic Papers

  1. On the compactness of the non-radial Sobolev space, Journal of Mathematical Analysis and Applications, 20230401
  2. Improvements and Generalizations of Two Hardy Type Inequalities and Their Applications to the Rellich Type Inequalities, MILAN JOURNAL OF MATHEMATICS, 90(2), 647-678, 202212
  3. ★, Critical Hardy inequality on the half-space via the harmonic transplantation, Calculus of Variations Partial Differential Equations, 61(4), 20220614
  4. Finsler Hardy inequalities, MATHEMATISCHE NACHRICHTEN, 293(12), 2370-2398, 202012
  5. Minimization problem associated with an improved Hardy-Sobolev type inequality, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 200, 202011
  6. REMARKS ON A LIMITING CASE OF HARDY TYPE INEQUALITIES, MATHEMATICAL INEQUALITIES & APPLICATIONS, 23(4), 1425-1440, 202010
  7. ★, Extremal functions of generalized critical Hardy inequalities, JOURNAL OF DIFFERENTIAL EQUATIONS, 267(4), 2594-2615, 20190805
  8. Weighted Hardy's inequality in a limiting case and the perturbed Kolmogorov equation, Appl. Anal., 98(10), 1875-1888, 20190727
  9. Scaling invariant Hardy type inequalities with non-standard remainder terms, Math. Inequal. Appl., 21(1), 77-90, 2018
  10. Some improvements for a class of the Caffarelli-Kohn-Nirenberg inequalities, Differential Integral Equations, 31(1-2), 57-74, 201801
  11. ★, Strauss's radial compactness and nonlinear elliptic equation involving a variable critical exponent, J. Funct. Spaces, 2018, 1-13, 2018
  12. ★, Scale invariance structures of the critical and the subcritical Hardy inequalities and their improvements, Calc. Var. Partial Differential Equations, 56(3), 56-69, 20170426
  13. Improved Rellich type inequalities in R^N, Geometric properties for parabolic and elliptic PDE's, Springer Proc. Math. Stat., 176, 241-255, 20160809
  14. Sublinear eigenvalue problems with singular weights related to the critical Hardy inequality, Electron. J. Differential Equations, 2016(2012), 1-12, 20160810
  15. A mean value property for polycaloric functions, Sci. Math. Jpn., 78(1), 103-112, 20150601

Invited Lecture, Oral Presentation, Poster Presentation

  1. The critical Hardy inequality on the half-space via harmonic transplantation, Megumi Sano, 2021/07, With Invitation, Japanese, Zoom
  2. Weighted Hardy's inequality in a limiting case and the perturbed Kolmogorov equation, Sano, Megumi, PDEs and Probability Theory - beyond boundaries -, 2021/06, With Invitation, English, Zoom
  3. Minimization problem associated with an improved Hardy-Sobolev inequality, Sano, Megumi, 2019 International Workshop on PDEs and Applications, 2019/10, With Invitation, English, Jeju National University
  4. A limiting case of the Hardy type inequalities via extrapolation method, Megumi Sano, RIMS workshop ``Geometric Aspects of Solutions to Partial Differential Equations", 2019/06, With Invitation, English, RIMS
  5. A limiting case of the Hardy type inequalities via extrapolation method, Megumi Sano, 6th Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's, 2019/05, With Invitation, English, Cortona, Italy
  6. A limiting case of the Hardy type inequalities via extrapolation method, Megumi Sano, NLPDE Seminar, 2019/05, With Invitation, Japanese, Kyoto University
  7. Minimization problems associated with embedding of the critical Sobolev spaces, Megumi Sano, Minisymposium ``Qualitative properties of solutions to Elliptic and Parabolic PDEs and related topics" at ``International Conference on Elliptic and Parabolic Problems", 2019/05, With Invitation, English, Gaeta, Italy
  8. Minimization problems associated with embedding of the critical Sobolev spaces, Megumi Sano, 2019/03, With Invitation, Japanese, Nagoya University
  9. Strauss's radial compactness and its application to nonlinear elliptic problem with variable critical exponent, Megumi Sano, The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 2018/07, With Invitation, English, National Taiwan University
  10. Sharp critical Rellich inequality in four dimension, Megumi Sano, Analysis Seminar, 2017/10, With Invitation, English, University of Napoli Federico II
  11. Strauss's radial compactness and nonlinear elliptic equation involving a variable critical exponent, Megumi Sano, CIME Summer School on "Geometry of PDE's and related problems", 2017/06, With Invitation, English, Italy

Awards

  1. 2015/07, Award for Young Mathematicians, KNU-OCU-PNU joint workshop

External Funds

Acceptance Results of Competitive Funds

  1. 2023/04/01, 2028/03/31
  2. Grant-in-Aid for Young Scientists, 2019/04/01, 2023/03/31
  3. Grant-in-Aid for Scientific Research (B), 2019/04/01, 2023/03/31
  4. Research Fellowship for Young Scientists, 2018/04/01, 2019/03/31
  5. Grant-in-Aid for Scientific Research (A), 2017/04/01, 2022/03/31
  6. Research Fellowship for Young Scientists, 2016/04/01, 2018/03/31