83 citations · 93 across the 15 of their papers we have counts for
17 papers
Weighted mixed-norm estimates for fractional parabolic equations with space-time nonlocal operators
Hongjie Dong, Junhee Ryu
We establish weighted mixed-norm estimates for fractional parabolic equations \begin{equation*} \partial_t^αu=Lu-λu+f \text{ in } (0,T)\times\mathbb{R}^d, \end{equation*} with nonl…
Nontangential Maximal Function estimates for the elliptic Mixed Boundary Value Problem with variable coefficients
Hongjie Dong, Martin Ulmer
We consider an elliptic operator with variable, merely bounded, and measurable coefficients on a Lipschitz domain, and study solutions to that attain given Neumann and D…
Singular-degenerate parabolic systems with the conormal boundary condition on the upper half space
Bekarys Bekmaganbetov, Hongjie Dong
We prove the well-posedness and regularity of solutions in mixed-norm weighted Sobolev spaces for a class of second-order parabolic and elliptic systems in divergence form in the h…
On nondivergence form linear parabolic and elliptic equations with degenerate coefficients
Hongjie Dong, Junhee Ryu
We establish the unique solvability in weighted mixed-norm Sobolev spaces for a class of degenerate parabolic and elliptic equations in the upper half space. The operators are in n…
Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem
Hongjie Dong, Seongmin Jeon
In this paper, we study solutions of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder , wh…
Refined regularity at critical points for linear elliptic equations
Jongkeun Choi, Hongjie Dong, Seick Kim
We investigate the regularity of solutions to linear elliptic equations in both divergence and non-divergence forms, particularly when the principal coefficients have Dini mean osc…
Regular boundary points and the Dirichlet problem for elliptic equations in double divergence form
Hongjie Dong, Dong-ha Kim, Seick Kim
We study the Dirichlet problem for second-order elliptic operators in double divergence form, which arise as formal adjoints of non-divergence form operators and include the statio…
The Dirichlet problem for second-order elliptic equations in non-divergence form with continuous coefficients: The two-dimensional case
Hongjie Dong, Dong-ha Kim, Seick Kim
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator in a bounded domain of . Assuming that the principal coefficients satisf…
Hopf-Oleinik lemma for elliptic equations in double divergence form
Hongjie Dong, Seick Kim, Boyan Sirakov
We establish, for the first time, a Zaremba-Hopf-Oleinik type boundary point lemma for uniformly elliptic partial differential equations in double divergence form, also known as st…
Boundary estimates for elliptic operators in divergence form with VMO coefficients
Hongjie Dong, Seongmin Jeon
We establish boundary regularity estimates for elliptic systems in divergence form with VMO coefficients. Additionally, we obtain nondegeneracy estimates of the Hopf-Oleinik type l…
Schauder type estimates for degenerate or singular parabolic systems with partially DMO coefficients
Hongjie Dong, Seongmin Jeon
We study elliptic and parabolic systems in divergence form with degenerate or singular coefficients. Under the conormal boundary condition on the flat boundary, we establish bounda…
Sobolev estimates for parabolic and elliptic equations in divergence form with degenerate coefficients
Hongjie Dong, Junhee Ryu
We study a class of degenerate parabolic and elliptic equations in divergence form in the upper half space . The leading coefficients are of the form , wher…
Elliptic and parabolic equations with rough boundary data in Sobolev spaces with degenerate weights
Bekarys Bekmaganbetov, Hongjie Dong
We investigate the inhomogeneous boundary value problem for elliptic and parabolic equations in divergence form in the half space , where the coefficients are measurab…
The Dirichlet problem for second-order elliptic equations in non-divergence form with continuous coefficients
Hongjie Dong, Dong-ha Kim, Seick Kim
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator in a bounded domain of . Under certain conditions on the coefficients of…
Regularity of elliptic equations in double divergence form and applications to Green's function estimates
Jongkeun Choi, Hongjie Dong, Dong-ha Kim +1
We investigate the regularity of elliptic equations in double divergence form, where the leading coefficients satisfying the Dini mean oscillation condition. We prove that the solu…
Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients
Hongjie Dong, Seongmin Jeon, Stefano Vita
In this paper, we study degenerate or singular elliptic equations in divergence form Whe…
On -estimates for a class of non-local elliptic equations
Hongjie Dong, Doyoon Kim
We consider non-local elliptic operators with kernel , where is a constant and is a bounded measurable function. By using a purely analytic meth…