101 citations · 792 across the 50 of their papers we have counts for
50 papers
Boundary blow-up solutions: gradient asymptotics and uniqueness
Seick Kim
Let be a bounded domain, and let be a nonnegative, nondecreasing function satisfying the Keller-Osserman condition. We study boundary blow-up solutions of…
A sign-changing Poisson kernel for a non-symmetric elliptic operator in a bounded domain
Seick Kim
We construct an explicit sign-changing Poisson kernel for a uniformly elliptic divergence form operator in the unit disk. The coefficient matrix is non-symmetric, and its skew-symm…
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…