MEGUMI SANO
Last Updated :2024/05/07
- 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
- The Mathematical Society of Japan
Educational Activity
Course in Charge
- 2024, Liberal Arts Education Program1, 2Term, Seminar in Basic Mathematics I
- 2024, Undergraduate Education, 1Term, Applied Mathematics II
- 2024, Undergraduate Education, 4Term, Engineering Mathematics C
- 2024, Graduate Education (Master's Program) , 1Term, Special Exercises on Electrical, Systems, and Control Engineering A
- 2024, Graduate Education (Master's Program) , 2Term, Special Exercises on Electrical, Systems, and Control Engineering A
- 2024, Graduate Education (Master's Program) , 3Term, Special Exercises on Electrical, Systems, and Control Engineering B
- 2024, Graduate Education (Master's Program) , 4Term, Special Exercises on Electrical, Systems, and Control Engineering B
- 2024, Graduate Education (Master's Program) , Academic Year, Special Study on Electrical, Systems, and Control Engineering
- 2024, Graduate Education (Master's Program) , 3Term, Mathematics C
- 2024, Graduate Education (Doctoral Program) , Academic Year, Special Study on Electrical, Systems, and Control Engineering
Research Activities
Academic Papers
- On the compactness of the non-radial Sobolev space, Journal of Mathematical Analysis and Applications, 20230401
- 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
- ★, Critical Hardy inequality on the half-space via the harmonic transplantation, Calculus of Variations Partial Differential Equations, 61(4), 20220614
- Finsler Hardy inequalities, MATHEMATISCHE NACHRICHTEN, 293(12), 2370-2398, 202012
- Minimization problem associated with an improved Hardy-Sobolev type inequality, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 200, 202011
- REMARKS ON A LIMITING CASE OF HARDY TYPE INEQUALITIES, MATHEMATICAL INEQUALITIES & APPLICATIONS, 23(4), 1425-1440, 202010
- ★, Extremal functions of generalized critical Hardy inequalities, JOURNAL OF DIFFERENTIAL EQUATIONS, 267(4), 2594-2615, 20190805
- Weighted Hardy's inequality in a limiting case and the perturbed Kolmogorov equation, Appl. Anal., 98(10), 1875-1888, 20190727
- Scaling invariant Hardy type inequalities with non-standard remainder terms, Math. Inequal. Appl., 21(1), 77-90, 2018
- Some improvements for a class of the Caffarelli-Kohn-Nirenberg inequalities, Differential Integral Equations, 31(1-2), 57-74, 201801
- ★, Strauss's radial compactness and nonlinear elliptic equation involving a variable critical exponent, J. Funct. Spaces, 2018, 1-13, 2018
- ★, Scale invariance structures of the critical and the subcritical Hardy inequalities and their improvements, Calc. Var. Partial Differential Equations, 56(3), 56-69, 20170426
- Improved Rellich type inequalities in R^N, Geometric properties for parabolic and elliptic PDE's, Springer Proc. Math. Stat., 176, 241-255, 20160809
- Sublinear eigenvalue problems with singular weights related to the critical Hardy inequality, Electron. J. Differential Equations, 2016(2012), 1-12, 20160810
- A mean value property for polycaloric functions, Sci. Math. Jpn., 78(1), 103-112, 20150601
Invited Lecture, Oral Presentation, Poster Presentation
- The critical Hardy inequality on the half-space via harmonic transplantation, Megumi Sano, 2021/07, With Invitation, Japanese, Zoom
- 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
- 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
- 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
- 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
- A limiting case of the Hardy type inequalities via extrapolation method, Megumi Sano, NLPDE Seminar, 2019/05, With Invitation, Japanese, Kyoto University
- 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
- Minimization problems associated with embedding of the critical Sobolev spaces, Megumi Sano, 2019/03, With Invitation, Japanese, Nagoya University
- 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
- Sharp critical Rellich inequality in four dimension, Megumi Sano, Analysis Seminar, 2017/10, With Invitation, English, University of Napoli Federico II
- 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
- 2015/07, Award for Young Mathematicians, KNU-OCU-PNU joint workshop
External Funds
Acceptance Results of Competitive Funds
- 2023/04/01, 2028/03/31
- Grant-in-Aid for Young Scientists, 2019/04/01, 2023/03/31
- Grant-in-Aid for Scientific Research (B), 2019/04/01, 2023/03/31
- Research Fellowship for Young Scientists, 2018/04/01, 2019/03/31
- Grant-in-Aid for Scientific Research (A), 2017/04/01, 2022/03/31
- Research Fellowship for Young Scientists, 2016/04/01, 2018/03/31