Last modified: October 3, 2017

Publications

Research papers

  1. K. Hirata, Existence and nonexistence of a positive solution of the Lane--Emden equation having a boundary singularity: the subcritical case, Monatsh. Math. (to appear)
  2. K. Hirata & T. Ono, Removable sets for continuous solutions of quasilinear elliptic equations with nonlinear source or absorption terms, Ann. Mat. Pura Appl. (to appear)
  3. K. Hirata, A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain, J. Anal. Math. (to appear)
  4. K. Hirata, Removable sets for subcaloric functions and solutions of semilinear heat equations with absorption, Hokkaido Math. J., vol. 45, pp. 195--222, (2016)
  5. 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)
  6. K. Hirata & T. Ono, Removable singularities and singular solutions of semilinear elliptic equations, Nonlinear Anal., vol. 105, pp. 10--23, (2014)
  7. K. Hirata, Removable singularities of semilinear parabolic equations, Proc. Amer. Math. Soc., vol. 142, no. 1, pp.157--171, (2014)
  8. 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)
  9. K. Hirata, Removable sets for continuous solutions of semilinear elliptic equations, Manuscripta Math., vol. 135, no. 1--2, pp. 245--262, (2011)
  10. K. Hirata, Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains, J. Math. Soc. Japan, vol. 62, no. 4, pp. 1043--1068, (2010)
  11. K. Hirata, Boundary behavior of solutions of the Helmholtz equation, Canad. Math. Bull., vol. 52, no. 4, pp. 555--563, (2009)
  12. 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)
  13. 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)
  14. 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)
  15. H. Aikawa & K. Hirata, Doubling conditions for harmonic measure in John domains, Ann. Inst. Fourier (Grenoble), vol. 58, no. 2, pp. 429--445, (2008)
  16. 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)
  17. 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)
  18. K. Hirata, Estimates for the products of the Green function and the Martin kernel, Nagoya Math. J., vol. 188, pp. 1--18, (2007)
  19. 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)
  20. K. Hirata, Boundary behaviour of quotients of Martin kernels, Proc. Edinb. Math. Soc., vol. 50, no. 2, pp. 377--388, (2007)
  21. 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)
  22. 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)
  23. K. Hirata, Sharpness of the Korányi approach region, Proc. Amer. Math. Soc., vol. 133, no. 8, pp. 2309--2317, (2005)
  24. 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

  1. K. Hirata, Two sided global estimates of heat kernels in Lipschitz domains, RIMS Kôkyûroku Bessatsu, vol. 43, pp. 29--45, (2013)
  2. 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)
  3. K. Hirata, Martin kernels of general domains, Adv. Stud. Pure Math., vol. 44, pp. 145--154, (2006)

RIMS kokyuroku

  1. K. Hirata, An a priori estimate for positive solutions of the Lane--Emden equation in a Lipschitz domain, RIMS kokyuroku 2041, pp. 227--233, (2016)
  2. K. Hirata, Limits at infinity of superharmonic functions and solutions of semilinear elliptic equations of Matukuma type, RIMS kokyuroku 1669, pp. 52--57, (2009)
  3. K. Hirata, On the boundary growth of superharmonic functions satisfying nonlinear inequalities, RIMS kokyuroku 1553, pp. 97--106, (2007)
  4. 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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