95 citations · 249 across the 21 of their papers we have counts for
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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…
Two-sided Gaussian estimates for fundamental solutions of second-order parabolic equations in non-divergence form
Seick Kim, Sungjin Lee, Georgios Sakellaris
We establish two-sided Gaussian bounds for the fundamental solution of second-order parabolic operators in non-divergence form under minimal regularity assumptions. Specifically, w…
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…
The Dirichlet problem for second-order elliptic equations in non-divergence form with continuous coefficients: The two-dimensional case
Hongjie Dong, Dong-ha Kim, Seick Kim
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator in a bounded domain of . Assuming that the principal coefficients satisf…
Recent progress on second-order elliptic and parabolic equations in double divergence form
Seick Kim
This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, a…
Hopf-Oleinik lemma for elliptic equations in double divergence form
Hongjie Dong, Seick Kim, Boyan Sirakov
We establish, for the first time, a Zaremba-Hopf-Oleinik type boundary point lemma for uniformly elliptic partial differential equations in double divergence form, also known as st…