5 papers
Global Hölder Solvability of parabolic equations on domains with capacity density conditions
Takanobu Hara
We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of g…
Uniformly Elliptic Equations on Domains with Capacity Density Conditions: Existence of Hölder Continuous Solutions and Homogenization Results
Takanobu Hara
This is a progress report on study of uniformly elliptic Poisson-type equations on domains with capacity density conditions (CDC domains). We give a brief summary of known facts of…
Global Hölder solvability of second order elliptic equations with locally integrable lower-order coefficients
Takanobu Hara
We prove the existence of globally Hölder continuous solutions to certain elliptic partial differential equations with lower-order terms. Our result is applicable to coefficients c…
Global Hölder solvability of linear and quasilinear Poisson equations
Takanobu Hara
We establish an existence result for globally continuous weak solutions to elliptic equations of the -Poisson type. This result significantly improves Theorem 8.30 in Gilbarg-Tr…
Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms
Takanobu Hara, Adisak Seesanea
We study the existence of positive solutions to quasilinear elliptic equations of the type \[ -Δ_{p} u = σu^{q} + μ\quad \text{in} \ \mathbb{R}^{n}, \] in the sub-natural growth ca…