20 citations · 80 across the 20 of their papers we have counts for
21 papers
Failure of zero extension in parabolic Sobolev spaces
Jongkeun Choi, Doyoon Kim, Kwan Woo
We show that spatial zero extension across the boundary may fail in parabolic Sobolev spaces , which can also be characterized as $$ L_p…
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…
Green functions of mixed boundary value problems for stationary Stokes systems in two dimensions
Jongkeun Choi, Minsuk Yang
We establish the existence, uniqueness, and various estimates for Green functions of mixed Dirichlet-conormal derivative problems for the stationary Stokes system with measurable c…
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…
Green functions for stationary Stokes systems with conormal derivative boundary condition in two dimensions
Jongkeun Choi, Doyoon Kim
We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.
Mixed boundary value problems for parabolic equations in Sobolev spaces with mixed-norms
Jongkeun Choi, Hongjie Dong, Zongyuan Li
We establish -estimates and solvability for mixed Dirichlet-conormal problems for parabolic equations in a cylindrical Reifenberg-flat domain with a rough time-dependent s…
Gradient estimates for Stokes and Navier-Stokes systems with piecewise DMO coefficients
Jongkeun Choi, Hongjie Dong, Longjuan Xu
We study stationary Stokes systems in divergence form with piecewise Dini mean oscillation coefficients and data in a bounded domain containing a finite number of subdomains with $…
Optimal regularity of mixed Dirichlet-conormal boundary value problems for parabolic operators
Jongkeun Choi, Hongjie Dong, Zongyuan Li
We obtain the regularity of solutions in Sobolev spaces for the mixed Dirichlet-conormal problem for parabolic operators in cylindrical domains with time-dependent separations, whi…
Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain
Jongkeun Choi, Hongjie Dong, Zongyuan Li
We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique solvability is obtained with being in the o…
Green functions for pressure of Stokes systems
Jongkeun Choi, Hongjie Dong
We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain , where . We construct the Green function whe…
Estimates for Green functions of Stokes systems in two dimensional domains
Jongkeun Choi, Doyoon Kim
We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwis…
Gradient estimates for Stokes systems in domains
Jongkeun Choi, Hongjie Dong
We study the stationary Stokes system with Dini mean oscillation coefficients in a domain having boundary. We prove that if is a weak solution of the sys…
Green functions of conormal derivative problems for stationary Stokes system
Jongkeun Choi, Hongjie Dong, Doyoon Kim
We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Gree…
Gradient estimates for Stokes systems with Dini mean oscillation coefficients
Jongkeun Choi, Hongjie Dong
We study the stationary Stokes system in divergence form. The coefficients are assumed to be merely measurable in one direction and have Dini mean oscillations in the other directi…
Conormal derivative problems for stationary Stokes system in Sobolev spaces
Jongkeun Choi, Hongjie Dong, Doyoon Kim
We prove the solvability in Sobolev spaces of the conormal derivative problem for the stationary Stokes system with irregular coefficients on bounded Reifenberg flat domains. The c…
Fundamental solutions for stationary Stokes systems with measurable coefficients
Jongkeun Choi, Minsuk Yang
We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space , $d \…
Weighted -estimates for higher order elliptic and parabolic systems with coefficients on Reifenberg flat domains
Jongkeun Choi, Doyoon Kim
We prove weighted -estimates for divergence type higher order elliptic and parabolic systems with irregular coefficients on Reifenberg flat domains. In particular, in the…
The Green function for the Stokes system with measurable coefficients
Jongkeun Choi, Ki-Ahm Lee
We study the Green function for the stationary Stokes system with bounded measurable coefficients in a bounded Lipschitz domain , . We construct the…
Green's functions for elliptic and parabolic systems with Robin-type boundary conditions
Jongkeun Choi, Seick Kim
The aim of this paper is to investigate Green's function for parabolic and elliptic systems satisfying a possibly nonlocal Robin-type boundary condition. We construct Green's funct…
Green's function for second order parabolic systems with Neumann boundary condition
Jongkeun Choi, Seick Kim
We study the Neumann Green's function for second order parabolic systems in divergence form with time-dependent measurable coefficients in a cylindrical domain $\mathcal{Q}=Ω\times…
Neumann functions for second order elliptic systems with measurable coefficients
Jongkeun Choi, Seick Kim
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We est…