116 citations · 577 across the 41 of their papers we have counts for
41 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…
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…
Painsight: An Extendable Opinion Mining Framework for Detecting Pain Points Based on Online Customer Reviews
Yukyung Lee, Jaehee Kim, Doyoon Kim +3
As the e-commerce market continues to expand and online transactions proliferate, customer reviews have emerged as a critical element in shaping the purchasing decisions of prospec…
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…