116 citations · 577 across the 41 of their papers we have counts for
38 papers · 1 filter
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…
Sobolev spaces and trace theorems for time-fractional evolution equations
Doyoon Kim, Kwan Woo
We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) spaces. To achieve this, we identify weighted Sobole…
Time fractional parabolic equations with partially SMO coefficients
Hongjie Dong, Doyoon Kim
We present the unique solvability in Sobolev spaces of time fractional parabolic equations in divergence and non-divergence forms. The leading coefficients are merely measurable in…
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.
Boundedness of non-local operators with spatially dependent coefficients and -estimates for non-local equations
Hongjie Dong, Pilgyu Jung, Doyoon Kim
We prove the boundedness of the non-local operator \[ \mathcal{L}^a u(x)=\int_{\mathbb{R}^d} \left(u(x+y)-u(x)-χ_α(y)\big(\nabla u(x),y\big)\right) a(x,y)\frac{dy}{|y|^{d+α}} \] fr…
Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces
Doyoon Kim, Kyeong-Hun Kim, Kwan Woo
We present weighted Sobolev spaces and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted pa…
Time fractional parabolic equations with measurable coefficients and embeddings for fractional parabolic Sobolev spaces
Hongjie Dong, Doyoon Kim
We consider time fractional parabolic equations in both divergence and non-divergence form when the leading coefficients are measurable functions of except for $…
Parabolic equations with unbounded lower-order coefficients in Sobolev spaces with mixed norms
Doyoon Kim, Seungjin Ryu, Kwan Woo
We prove the Lp,q-solvability of parabolic equations in divergence form with full lower-order terms. The coefficients and non-homogeneous terms belong to mixed Lebesgue spaces with…
An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives
Hongjie Dong, Doyoon Kim
We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are m…
Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients
Hongjie Dong, Doyoon Kim, Tuoc Phan
We consider Stokes systems with measurable coefficients and Lions-type boundary conditions. We show that, in contrast to the Dirichlet boundary conditions, local boundary mixed-nor…
-estimates for time fractional parabolic equations in divergence form with measurable coefficients
Hongjie Dong, Doyoon Kim
In this paper, we establish estimates and solvability for time fractional divergence form parabolic equations in the whole space when leading coefficients are merely measurab…
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…
Parabolic Systems with measurable coefficients in weighted Sobolev spaces
Doyoon Kim, Kyeong-Hun Kim, Kijung Lee
In this paper we present a weighted -theory of parabolic systems on a half space. The leading coefficients are assumed to be only measurable in and have small bounded mean…
-estimates for time fractional parabolic equations with coefficients measurable in time
Hongjie Dong, Doyoon Kim
We establish the -solvability for time fractional parabolic equations when coefficients are merely measurable in the time variable. In the spatial variables, the leading coeff…
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…
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…
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…
Weighted -estimates for stationary Stokes system with partially BMO coefficients
Hongjie Dong, Doyoon Kim
We prove the unique solvability of solutions in Sobolev spaces to the stationary Stokes system on a bounded Reifenberg flat domain when the coefficients are partially BMO functions…
-estimates for stationary Stokes system with coefficients measurable in one direction
Hongjie Dong, Doyoon Kim
We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a prior…
On -estimates for elliptic and parabolic equations with weights
Hongjie Dong, Doyoon Kim
We prove generalized Fefferman-Stein type theorems on sharp functions with weights in spaces of homogeneous type with either finite or infinite underlying measure. We then ap…
Neumann problem for non-divergence elliptic and parabolic equations with BMO coefficients in weighted Sobolev spaces
Hongjie Dong, Doyoon Kim, Hong Zhang
We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition.…
On the impossibility of estimates for elliptic equations with piecewise constant coefficients
Hongjie Dong, Doyoon Kim
In this paper, we present counterexamples showing that for any , , there is a non-divergence form uniformly elliptic operator with piecewise constant coef…
Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces
Hongjie Dong, Doyoon Kim
We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the…
Boundary value problems for parabolic operators in a time-varying domain
Sungwon Cho, Hongjie Dong, Doyoon Kim
We prove the existence of unique solutions to the Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence for…