7 citations · 20 across the 9 of their papers we have counts for
11 papers
Boundary Harnack principle for abstract supersolutions on uniform domains
Takanobu Hara
We develop an axiomatic approach to the boundary Harnack principle on diameter-uniform domains in proper doubling metric measure spaces. Under critical-density and upper-contractio…
Weighted and nonlocal Poisson equations on domains with capacity density conditions
Takanobu Hara
We establish necessary and sufficient conditions for global Hölder solvability of weighted Poisson equations and related fractional problems. On domains satisfying a capacity densi…
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…
Strong barriers for weighted quasilinear equations
Takanobu Hara
In potential theory, use of barriers is one of the most important techniques. We construct strong barriers for weighted quasilinear elliptic operators. There are two applications:…
A stability result for elliptic equations with singular nonlinearity and its applications to homogenization problems
Takanobu Hara
We consider model semilinear elliptic equations of the type \[ \begin{cases} - \mathrm{div} (A(x) \nabla u) = f u^{- λ}, \quad u > 0 \quad \text{in} \ Ω, \\ u \in H_{0}^{1}(Ω), \en…
Trace inequalities of the Sobolev type and nonlinear Dirichlet problems
Takanobu Hara
We discuss the solvability of Dirichlet problems of the type in ; on , where is a bounded domain in , is a…
Quasilinear elliptic equations with sub-natural growth terms in bounded domains
Takanobu Hara
We consider the existence of positive solutions to weighted quasilinear elliptic differential equations of the type \[ \begin{cases} - Δ_{p, w} u = σu^{q} & \text{in }, \\ u = 0…
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…