## 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

- Mathematical Society of Japan

## Educational Activity

### Course in Charge

- 2024, Undergraduate Education, 4Term, Analysis ＩＩ
- 2024, Undergraduate Education, 2Term, Analysis III
- 2024, Undergraduate Education, 4Term, Exercises in Analysis ＩＩ
- 2024, Undergraduate Education, 1Term, Exercises in Analysis B
- 2024, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
- 2024, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
- 2024, Graduate Education (Master's Program) , Academic Year, Seminar on Complex Analysis and Functional Equations
- 2024, Graduate Education (Master's Program) , 1Term, Mathematical Analysis A
- 2024, Graduate Education (Master's Program) , 2Term, Mathematical Analysis B
- 2024, Graduate Education (Master's Program) , 4Term, Topics in Mathematical Analysis C
- 2024, Graduate Education (Master's Program) , 3Term, Topics in Mathematical Analysis D
- 2024, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
- 2024, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
- 2024, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
- 2024, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
- 2024, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

## Research Activities

### Academic Papers

- 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
- Boundary growth rates and exceptional sets for superharmonic functions on the real hyperbolic ball, JOURNAL OF GEOMETRIC ANALYSIS, 31(11), 10586-10602, 202111
- The Dirichlet problem for sublinear elliptic equations with source, BULLETIN DES SCIENCES MATHEMATIQUES, 171, 1-20 (No. 103030), 202110
- Boundary growth rates and the size of singular sets for superharmonic functions satisfying a nonlinear inequality, ARCHIV DER MATHEMATIK, 116(3), 335-344, 202103
- Boundary estimates for superharmonic functions and solutions of semilinear elliptic equations with source, COLLECTANEA MATHEMATICA, 72(1), 43-61, 202101
- Global integrability of supertemperatures, MATHEMATISCHE ZEITSCHRIFT, 296(3-4), 1049-1063, 202012
- 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
- Two-sided estimates for positive solutions of superlinear elliptic boundary value problems, BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 98(3), 465-473, 201812
- 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
- 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
- Removable sets for subcaloric functions and solutions of semilinear heat equations with absorption, HOKKAIDO MATHEMATICAL JOURNAL, 45(2), 195-222, 201606
- 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
- Removable singularities and singular solutions of semilinear elliptic equations, NONLINEAR ANALYSIS. THEORY, METHODS & APPLICATIONS, 105, 10-23, 201408
- Removable singularities of semilinear parabolic equations, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 142(1), 157-171, 201401
- Two sided global estimates of heat kernels in Lipschitz domains, RIMS KOKYUROKU BESSATSU, B43, 29-45, 201309
- 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
- Removable sets for continuous solutions of semilinear elliptic equations, MANUSCRIPTA MATHEMATICA, 135(1-2), 245-262, 201105
- Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(8), 4007-4025, 201103
- Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 62(4), 1043-1068, 201010
- Boundary behavior of solutions of the Helmholtz equation, CANADIAN MATHEMATICAL BULLETIN, 52(4), 555-563, 200912
- Boundary behavior of superharmonic functions satisfying nonlinear inequalities in a planar smooth domain, JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 87(2), 253-261, 200910
- Limits at infinity of superharmonic functions and solutions of semilinear elliptic equations of Matukuma type, POTENTIAL ANALYSIS, 30(2), 165-177, 200902
- Global estimates for non-symmetric Green type functions with applications to the p-Laplace equation, POTENTIAL ANALYSIS, 29(3), 221-239, 200811
- The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations, MATHEMATISCHE ANNALEN, 340(3), 625-645, 200803
- 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
- Doubling conditions for harmonic measure in John domains, ANNALES DE L'INSTITUT FOURIER, 58(2), 429-445, 2008
- Estimates for the products of the Green function and the Martin kernel, NAGOYA MATHEMATICAL JOURNAL, 188, 1-18, 200712
- Boundary behaviour of quotients of Martin kernels, PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. SERIES II, 50(2), 377-388, 200706
- Martin boundary points of cones generated by spherical John regions, ANNALES ACADEMIA SCIENTIARUM FENNICA. MATHEMATICA, 32(2), 289-300, 2007
- Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrodinger problems in uniform cones, JOURNAL D'ANALYSE MATHEMATIQUE, 99, 309-332, 200612
- Martin kernels of general domains, ADVANCED STUDIES IN PURE MATHEMATICS, 44, 145-154, 200608
- Martin boundary points of a John domain and unions of convex sets, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 58(1), 247-274, 200601
- Sharpness of the Koranyi approach region, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 133(8), 2309-2317, 200503
- 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

- 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

- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Boundary behavior of superharmonic functions, Kentaro Hirata, The 9th Hokkaido University-Seoul National University Joint Symposium, 2007/02/23, Without Invitation, English, Hokkaido University
- 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
- 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
- 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
- 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
- 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