16 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…