List of Papers

Last modified: December 13, 2021

Publications

Research papers

K. Hirata, Boundary growth rates and exceptional sets for superharmonic functions on the real hyperbolic ball, J. Geom. Anal., vol. 31, pp. 10586--10602, (2021)
K. Hirata & A. Seesanea, The Dirichlet problem for sublinear elliptic equations with source, Bull. Sci. Math., vol. 171, Paper No. 103030, 20, (2021)
K. Hirata, Boundary growth rates and the size of singular sets for superharmonic functions satisfying a nonlinear inequality, Arch. Math., vol. 116, pp. 335--344, (2021)
K. Hirata, Boundary estimates for superharmonic functions and solutions of semilinear elliptic equations with source, Collect. Math., vol. 72, pp. 43--61, (2021)
H. Aikawa & T. Hara & K. Hirata, Global integrability of supertemperatures, Math. Z., vol. 296, pp. 1049--1063, (2020)
K. Hirata, A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain, J. Anal. Math., vol. 138, pp. 441--463, (2019)
K. Hirata, Two-sided estimates for positive solutions of superlinear elliptic boundary value problems, Bull. Aust. Math. Soc., vol. 98, pp. 465--473, (2018)
K. Hirata, Existence and nonexistence of a positive solution of the Lane--Emden equation having a boundary singularity: the subcritical case, Monatsh. Math., vol. 186, pp. 635--652, (2018)
K. Hirata & T. Ono, Removable sets for continuous solutions of quasilinear elliptic equations with nonlinear source or absorption terms, Ann. Mat. Pura Appl., vol. 197, no. 1, pp. 41--59, (2018)
K. Hirata, Removable sets for subcaloric functions and solutions of semilinear heat equations with absorption, Hokkaido Math. J., vol. 45, pp. 195--222, (2016)
K. Hirata, Positive solutions with a time-independent boundary singularity of semilinear heat equations in bounded Lipschitz domains, Nonlinear Anal., vol. 134, pp. 144--163, (2016)
K. Hirata & T. Ono, Removable singularities and singular solutions of semilinear elliptic equations, Nonlinear Anal., vol. 105, pp. 10--23, (2014)
K. Hirata, Removable singularities of semilinear parabolic equations, Proc. Amer. Math. Soc., vol. 142, no. 1, pp.157--171, (2014)
K. Hirata, Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains, Trans. Amer. Math. Soc., vol. 363, no. 8, pp. 4007--4025, (2011)
K. Hirata, Removable sets for continuous solutions of semilinear elliptic equations, Manuscripta Math., vol. 135, no. 1--2, pp. 245--262, (2011)
K. Hirata, Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains, J. Math. Soc. Japan, vol. 62, no. 4, pp. 1043--1068, (2010)
K. Hirata, Boundary behavior of solutions of the Helmholtz equation, Canad. Math. Bull., vol. 52, no. 4, pp. 555--563, (2009)
K. Hirata, Boundary behavior of superharmonic functions satisfying nonlinear inequalities in a planar smooth domain, J. Aust. Math. Soc., vol. 87, pp. 253--261, (2009)
K. Hirata, Limits at infinity of superharmonic functions and solutions of semilinear elliptic equations of Matukuma type, Potential Anal., vol. 30, no. 2, pp. 165--177, (2009)
K. Hirata, Global estimates for non-symmetric Green type functions with applications to the p-Laplace equation, Potential Anal., vol. 29, no. 3, pp. 221--239, (2008)
H. Aikawa & K. Hirata, Doubling conditions for harmonic measure in John domains, Ann. Inst. Fourier (Grenoble), vol. 58, no. 2, pp. 429--445, (2008)
K. Hirata, On the existence of positive solutions of singular nonlinear elliptic equations with Dirichlet boundary conditions, J. Math. Anal. Appl., vol. 338, no. 2, pp. 885--891, (2008)
K. Hirata, The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations, Math. Ann., vol. 340, no. 3, pp. 625--645, (2008)
K. Hirata, Estimates for the products of the Green function and the Martin kernel, Nagoya Math. J., vol. 188, pp. 1--18, (2007)
K. Hirata, Martin boundary points of cones generated by spherical John regions, Ann. Acad. Sci. Fenn. Math., vol. 32, no.2, pp. 289--300, (2007)
K. Hirata, Boundary behaviour of quotients of Martin kernels, Proc. Edinb. Math. Soc., vol. 50, no. 2, pp. 377--388, (2007)
K. Hirata, Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrödinger problems in uniform cones, J. Anal. Math., vol. 99, pp. 309--332, (2006)
H. Aikawa & K. Hirata & T. Lundh, Martin boundary points of a John domain and unions of convex sets, J. Math. Soc. Japan, vol. 58, no. 1, pp. 247--274, (2006)
K. Hirata, Sharpness of the Korányi approach region, Proc. Amer. Math. Soc., vol. 133, no. 8, pp. 2309--2317, (2005)
K. Hirata, Characterizations of M-harmonic α-Bloch and BMO functions on the unit ball of Cⁿ, Complex Var. Theory Appl., vol. 49, no. 7-9, pp. 583--594, (2004)

Proceedings

K. Hirata, Two sided global estimates of heat kernels in Lipschitz domains, RIMS Kôkyûroku Bessatsu, vol. 43, pp. 29--45, (2013)
K. Hirata, Admissible boundary limits of Green potentials satisfying nonlinear inequalities in the unit ball of Cⁿ, Topics in Finite or Infinite Dimensional Complex Analysis, Tohoku University Press, pp. 111--121, (2013)
K. Hirata, Martin kernels of general domains, Adv. Stud. Pure Math., vol. 44, pp. 145--154, (2006)

RIMS kokyuroku

K. Hirata, An a priori estimate for positive solutions of the Lane--Emden equation in a Lipschitz domain, RIMS kokyuroku 2041, pp. 227--233, (2017)
K. Hirata, Limits at infinity of superharmonic functions and solutions of semilinear elliptic equations of Matukuma type, RIMS kokyuroku 1669, pp. 52--57, (2009)
K. Hirata, On the boundary growth of superharmonic functions satisfying nonlinear inequalities, RIMS kokyuroku 1553, pp. 97--106, (2007)
H. Aikawa & K. Hirata & T. Lundh, Martin boundary for union of convex sets, RIMS kokyuroku 1293, pp. 1--14, (2002)

Doctoral Thesis (advised by Prof. Hiroaki Aikawa)

Invariant harmonic functions in the unit ball of Cⁿ and Martin kernels of general domains in Rⁿ

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