9 papers
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…
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…
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…
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…
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…