13 papers
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…
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…
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…
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…
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…
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…