2 citations · 2 across the 4 of their papers we have counts for
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-estimates of the conormal derivative problem for parabolic equations with time measurable coefficients and -weights
Hongjie Dong, Pilgyu Jung, Doyoon Kim
This paper investigates weighted mixed-norm estimates for divergence-type parabolic equations on Reifenberg-flat domains with the conormal derivative boundary condition. The leadin…
Fabes-Stroock approach to higher integrability of Green's functions and ABP estimates with drift
Pilgyu Jung, Kwan Woo
We explore the higher integrability of Green's functions associated with the second-order elliptic equation in a bounded domain $Ω\subset \mathbb{R}^…
-estimates for parabolic equations in divergence form with a half-time derivative
Pilgyu Jung, Doyoon Kim
We establish the unique solvability of solutions in Sobolev spaces to linear parabolic equations in a more general form than those in the literature. A distinguishing feature of ou…
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…