23 citations · 157 across the 57 of their papers we have counts for
7 papers · 1 filter
Cordes-Nirenberg type estimates for nonlocal parabolic equations
Yong-Cheol Kim, Ki-Ahm Lee
In this paper, we obtain Cordes-Nirenberg type estimates for nonlocal parabolic equations on the more flexible solution space $L^{\iy}_T(L^1_{\om})$ than the classical solution spa…
Harnack inequality for nondivergent parabolic operators on Riemannian manifolds
Seick Kim, Soojung Kim, Ki-Ahm Lee
We consider second-order linear parabolic operators in non-divergence form that are intrinsically defined on Riemannian manifolds. In the elliptic case, Cabré proved a global Krylo…
Fully Degenerate Monge Ampére Equations
Panagiota Daskalopoulos, Ki-ahm Lee
In this paper, we consider the following nonlinear eigenvalue problem for the Monge-Ampére equation: find a non-negative weakly convex classical solution satisfying {equation*}…
Long time existence of Smooth solution for the porous medium equation in a bounded domain
Sunghoon Kim
In this paper, we are going to show the long time existence of the smooth solution for the porous medium equations in a smooth bounded domain: {equation} {cases} u_t=\La u^m\quad\t…
Highly Oscillating Thin Obstacles
Ki-ahm Lee, Martin Strömqvist, Minha Yoo
The focus of this paper is on a thin obstacle problem where the obstacle is defined on the intersection between a hyper-plane in and a periodic perforation $\mat…
Asymptotic Behavior in Degenerate Parabolic Fully Nonlinear equations and its application to Elliptic Eigenvalue Problems
Soojung Kim, Ki-ahm Lee
We study the asymptotic behavior of the nonlinear parabolic flows when $t\ra \infty$ for , and the geometric properties for solutions of the following e…
Homogenization of the boundary value for the Dirichlet Problem
Sunghan Kim, Ki-ahm Lee, Henrik Shahgholian
In this paper, we give a mathematically rigorous proof of the averaging behavior of oscillatory surface integrals. Based on ergodic theory, we find a sharp geometric condition whic…