Research keywords (2)：
viscosity solutions
, Fully nonlinear PDE
Research theme for competitive and other funds (5)：
2022 - 2026 Research on the Quantitative Properties and the Singularities for Solutions to k-Hessian equations and k-curvature equations
2013 - 2017 Analysis on Behavior and Singularities of Solutions to Fully Nonlinear Elliptic and Parabolic Partial Differential Equations
2010 - 2013 Analysis on Fully Nonlinear Elliptic and Parabolic Partial Differential Equations and its Applications
2010 - 2012 Analysis on the Solvability of Boundary Value Problem and the Behavior of Solutions to Fully Nonlinear Partial Differential Equations
2004 - 2007 Solvability of Boundary Value Problems and Analysis on the Behavior of Solutions of Fully Nonlinear Elliptic and Parabolic Partial Differential Equations
Papers (24)：
Kazuhiro Takimoto and Yuxiao Zhang. Asymptotic behavior near the boundary of a large solution to semilinear Poisson equation with double-power nonlinearity. Acta Mathematica Scientia. 2024. 44. 6. 2083-2098
Kazuhiro Takimoto. The exterior Dirichlet problem for the generalized parabolic k-Hessian equations. Geometric Aspects on Partial Differential Equations, RIMS Kokyuroku. 2023. 2251. 29-42
Kazuhiro Takimoto. Exact principal blowup rate near the boundary of boundary blowup solutions to k-curvature equation. Manuscripta Mathematica. 2022. 168. 3-4. 351-369
Kazuhiro Takimoto. Second order boundary estimate of boundary blowup solutions to k-Hessian equation. Journal of Mathematical Analysis and Applications. 2021. 500. 2. 1-12
On the exterior Dirichlet problem for the generalized parabolic k-Hessian equations
(2024 Japan-Korea Workshop on Nonlinear PDEs and Its Applications 2024)
Higher order estimate near the boundary of a large solution to semilinear Poisson equation with double-power like nonlinearity
(Meeting of the Mathematical Society of Japan 2023)
Blowup rate near the boundary of boundary blowup solutions to $k$-Hessian equation and $k$-curvature equation
(13th AIMS International Conference on Dynamical Systems, Differential Equations and Applications 2023)
The exterior Dirichlet problem for the generalized parabolic k-Hessian equations
(Geometric Aspects on Partial Differential Equations 2022)
Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions
(Tuesday Seminar of Analysis 2022)
