KENTARO HIRATA

Last Updated :2024/06/07

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

Basic Information

Academic Degrees

  • Doctor of Science, Shimane University
  • Master, Shimane University

Research Fields

  • Mathematical and physical sciences;Mathematics;Basic analysis

Research Keywords

  • Potential Theory

Affiliated Academic Societies

Educational Activity

Course in Charge

  1. 2024, Undergraduate Education, 4Term, Analysis II
  2. 2024, Undergraduate Education, 2Term, Analysis III
  3. 2024, Undergraduate Education, 4Term, Exercises in Analysis II
  4. 2024, Undergraduate Education, 1Term, Exercises in Analysis B
  5. 2024, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  6. 2024, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  7. 2024, Graduate Education (Master's Program) , Academic Year, Seminar on Complex Analysis and Functional Equations
  8. 2024, Graduate Education (Master's Program) , 1Term, Mathematical Analysis A
  9. 2024, Graduate Education (Master's Program) , 2Term, Mathematical Analysis B
  10. 2024, Graduate Education (Master's Program) , 4Term, Topics in Mathematical Analysis C
  11. 2024, Graduate Education (Master's Program) , 3Term, Topics in Mathematical Analysis D
  12. 2024, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
  13. 2024, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
  14. 2024, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
  15. 2024, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
  16. 2024, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

Research Activities

Academic Papers

  1. Removable singularities for quasilinear elliptic equations with source terms involving the solution and its gradient, BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 53(3), 787-800, 202209
  2. Boundary growth rates and exceptional sets for superharmonic functions on the real hyperbolic ball, JOURNAL OF GEOMETRIC ANALYSIS, 31(11), 10586-10602, 202111
  3. The Dirichlet problem for sublinear elliptic equations with source, BULLETIN DES SCIENCES MATHEMATIQUES, 171, 1-20 (No. 103030), 202110
  4. Boundary growth rates and the size of singular sets for superharmonic functions satisfying a nonlinear inequality, ARCHIV DER MATHEMATIK, 116(3), 335-344, 202103
  5. Boundary estimates for superharmonic functions and solutions of semilinear elliptic equations with source, COLLECTANEA MATHEMATICA, 72(1), 43-61, 202101
  6. Global integrability of supertemperatures, MATHEMATISCHE ZEITSCHRIFT, 296(3-4), 1049-1063, 202012
  7. A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain, JOURNAL D'ANALYSE MATHEMATIQUE, 138(1), 441-463, 201910
  8. Two-sided estimates for positive solutions of superlinear elliptic boundary value problems, BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 98(3), 465-473, 201812
  9. Existence and nonexistence of a positive solution of the Lane-Emden equation having a boundary singularity: the subcritical case, MONATSHEFTE FUR MATHEMATIK, 186(4), 635-652, 201808
  10. Removable sets for continuous solutions of quasilinear elliptic equations with nonlinear source or absorption terms, ANNALI DI MATEMATICA PURA ED APPLICATA, 197(1), 41-59, 201801
  11. Removable sets for subcaloric functions and solutions of semilinear heat equations with absorption, HOKKAIDO MATHEMATICAL JOURNAL, 45(2), 195-222, 201606
  12. Positive solutions with a time-independent boundary singularity of semilinear heat equations in bounded Lipschitz domains, NONLINEAR ANALYSIS. THEORY, METHODS & APPLICATIONS, 134, 144-163, 201603
  13. Removable singularities and singular solutions of semilinear elliptic equations, NONLINEAR ANALYSIS. THEORY, METHODS & APPLICATIONS, 105, 10-23, 201408
  14. Removable singularities of semilinear parabolic equations, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 142(1), 157-171, 201401
  15. Two sided global estimates of heat kernels in Lipschitz domains, RIMS KOKYUROKU BESSATSU, B43, 29-45, 201309
  16. Admissible boundary limits of Green potentials satisfying nonlinear inequalities in the unit ball of C^n, TOPICS IN FINITE OR INFINITE DIMENSIONAL COMPLEX ANALYSIS, 111-121, 201301
  17. Removable sets for continuous solutions of semilinear elliptic equations, MANUSCRIPTA MATHEMATICA, 135(1-2), 245-262, 201105
  18. Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(8), 4007-4025, 201103
  19. Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 62(4), 1043-1068, 201010
  20. Boundary behavior of solutions of the Helmholtz equation, CANADIAN MATHEMATICAL BULLETIN, 52(4), 555-563, 200912
  21. Boundary behavior of superharmonic functions satisfying nonlinear inequalities in a planar smooth domain, JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 87(2), 253-261, 200910
  22. Limits at infinity of superharmonic functions and solutions of semilinear elliptic equations of Matukuma type, POTENTIAL ANALYSIS, 30(2), 165-177, 200902
  23. Global estimates for non-symmetric Green type functions with applications to the p-Laplace equation, POTENTIAL ANALYSIS, 29(3), 221-239, 200811
  24. The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations, MATHEMATISCHE ANNALEN, 340(3), 625-645, 200803
  25. On the existence of positive solutions of singular nonlinear elliptic equations with Dirichlet boundary conditions, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 338(2), 885-891, 200802
  26. Doubling conditions for harmonic measure in John domains, ANNALES DE L'INSTITUT FOURIER, 58(2), 429-445, 2008
  27. Estimates for the products of the Green function and the Martin kernel, NAGOYA MATHEMATICAL JOURNAL, 188, 1-18, 200712
  28. Boundary behaviour of quotients of Martin kernels, PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. SERIES II, 50(2), 377-388, 200706
  29. Martin boundary points of cones generated by spherical John regions, ANNALES ACADEMIA SCIENTIARUM FENNICA. MATHEMATICA, 32(2), 289-300, 2007
  30. Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrodinger problems in uniform cones, JOURNAL D'ANALYSE MATHEMATIQUE, 99, 309-332, 200612
  31. Martin kernels of general domains, ADVANCED STUDIES IN PURE MATHEMATICS, 44, 145-154, 200608
  32. Martin boundary points of a John domain and unions of convex sets, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 58(1), 247-274, 200601
  33. Sharpness of the Koranyi approach region, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 133(8), 2309-2317, 200503
  34. Characterizations of M-harmonic a-Bloch and BMO functions on the unit ball of C^n, COMPLEX VARIABLES. THEORY AND APPLICATION, 49(7-9), 583-594, 200406

Publications such as books

  1. 2013, Potential theory and its related fields, Research Institute for Mathematical Sciences, Kyoto University, Compilation, English, Kentaro Hirata (edited)

Invited Lecture, Oral Presentation, Poster Presentation

  1. Equivalent properties to a priori estimates for positive solutions of quasilinear elliptic equations with reaction terms, Kentaro Hirata, The POSTECH Conference 2022 on Complex Analytic Geometry, 2022/07/19, With Invitation, English, Posco international center in Pohang University of Science and Technology
  2. Positive solutions of semilinear elliptic equations with respect to the Schrödinger equation, Kentaro Hirata, Asia-Pacific Analysis and PDF seminar, 2021/12/13, With Invitation, English, Online on Zoom
  3. Boundary estimates for positive solutions of semilinear elliptic equations with source, Kentaro Hirata, Potential Theory and its Related Fields 2019, 2019/02/13, Without Invitation, English, Hokkaido University
  4. Removable isolated boundary singularities of positive solutions of semilinear elliptic equations in a Lipschitz domain, Hirata, Kentaro, The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 2018/07/08, With Invitation, English, National Taipei University
  5. A Carleson estimate for positive solutions of the Lane-Emden equation in a Lipschitz domain, Kentaro Hirata, Potential Analysis and its Related Fields 2017, 2017/09/21, With Invitation, English, Hokkaido University
  6. Heat kernel estimates and growth estimates of solutions of semilinear heat equations, Kentaro Hirata, RIMS meeting: Potential Theory and its Related Fields, 2012/09/07, Without Invitation, English, Kyoto University
  7. Admissible boundary limits of Green potentials satisfying nonlinear inequalities in the unit ball of C^n, Kentaro Hirata, The 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, 2011/12/14, With Invitation, English, Hiroshima Aster Plaza
  8. Boundary behavior of superharmonic functions satisfying nonlinear inequalities, Kentaro Hirata, The 11th Northeastern Symposium on Mathematical Analysis, 2010/02/23, With Invitation, English, Hokkaido University
  9. Boundary behavior of superharmonic functions satisfying nonlinear inequalities, Kentaro Hirata, The XXIst Rolf Nevanlinna Colloquium, 2009/09/10, With Invitation, English, Clock Tower Centennial Hall in Kyoto University
  10. Upper and lower estimates for parabolic Green functions in Lipschitz domains, Kentaro Hirata, International Workshop on Potential Theory 2009, 2009/09/01, Without Invitation, English, Hokkaido University
  11. Boundary behavior of superharmonic functions satisfying nonlinear inequalities in the unit disk, Kentaro Hirata, The 11th Conference on Real and Complex Analysis (Korea-Japan), 2008/02/18, Without Invitation, English, Hiroshima University
  12. Boundary behavior of superharmonic functions, Kentaro Hirata, The 9th Hokkaido University-Seoul National University Joint Symposium, 2007/02/23, Without Invitation, English, Hokkaido University
  13. On the boundary growth of superharmonic functions satisfying nonlinear inequalities, Kentaro Hirata, Finland-Japan Joint Seminar on Analysis, 2006/12/12, Without Invitation, English, Hiroshima University
  14. Estimates for the Green function and applications, Kentaro Hirata, The 9th Conference on Real and Complex Analysis (Korea-Japan), 2005/12/15, Without Invitation, English, Hiroshima University
  15. Boundary behavior of Martin kernels, Kentaro Hirata, The 8th Conference on Real and Complex Analysis (Korea-Japan), 2004/12/13, Without Invitation, English, Hiroshima University
  16. An estimate for the product of the Green function and the Martin kernel, Kentaro Hirata, International Workshop on Potential Theory, 2004/08/24, Without Invitation, English, Shimane University
  17. Sharpness of the Korányi approach region, Kentaro Hirata, The 7th Conference on Real and Complex Analysis (Korea-Japan), 2003/10/16, Without Invitation, English, Hiroshima University