Ki-Ahm Lee

activity

20102023

most citedThe Wiener criterion for nonlocal Dirichlet problems

23 citations · 157 across the 57 of their papers we have counts for

collaborators

59 papers

math.DG2023

On the uniqueness of energy-minimizing curves in constrained spaces

Ki-Ahm Lee, Taehun Lee

In this paper, we investigate energy-minimizing curves with fixed endpoints $p$ and $q$ in a constrained space. We prove that when one of the endpoints, say $p$ , is fixed, the set…

math.AP2023

The Wiener criterion for fully nonlinear elliptic equations

Ki-Ahm Lee, Se-Chan Lee

We study the boundary continuity of solutions to fully nonlinear elliptic equations. We first define a capacity for operators in non-divergence form and derive several capacitary e…

math.AP2022

The fractional $p$ -Laplacian on hyperbolic spaces

Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee

We present three equivalent definitions of the fractional $p$ -Laplacian $(- Δ_{H^{n}})_{p}^{s}$ , $0 < s < 1$ , $p > 1$ , with normalizing constants, on hyperbolic spaces. The expli…

math.AP2022

Global regularity results for a class of singular/degenerate fully nonlinear elliptic equations

Sumiya Baasandorj, Sun-Sig Byun, Ki-Ahm Lee +1

We provide the Alexandroff-Bakelman-Pucci estimate and global $C^{1, α}$ -regularity for a class of singular/degenerate fully nonlinear elliptic equations. We also derive the existe…

math.AP2022

C^{1,α}-regularity for a class of degenerate/singular fully nonlinear elliptic equations

Sumiya Baasandorj, Sun-Sig Byun, Ki-Ahm Lee +1

We establish an optimal C^{1,α}-regularity for viscosity solutions of degenerate/singular fully nonlinear elliptic equations by finding minimal regularity requirements on the assoc…

math.AP2022★ 23 cited

The Wiener criterion for nonlocal Dirichlet problems

Minhyun Kim, Ki-Ahm Lee, Se-Chan Lee

We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s \in (0, 1)$ and summability $p > 1$ . We es…

math.AP2021★ 1 cited

Uniform Integrability in Periodic Homogenization of Fully Nonlinear Equations

Sunghan Kim

This paper is devoted to the study of uniform $W^{1, \frac{n p}{n - p}}$ - and $W^{2, p}$ -estimates for viscosity solutions to fully nonlinear, uniformly elliptic, periodic homogenizatio…

math.AP2021★ 3 cited

Robust near-diagonal Green function estimates

Moritz Kassmann, Minhyun Kim, Ki-Ahm Lee

We prove sharp near-diagonal pointwise bounds for the Green function $G_{Ω} (x, y)$ for nonlocal operators of fractional order $α \in (0, 2)$ . The novelty of our results is two-fold: the…

math.AP2021★ 1 cited

Harnack inequality for fractional Laplacian-type operators on hyperbolic spaces

Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee

We establish the Krylov--Safonov theory for a large class of nonlocal operators of order $2 s \in (0, 2)$ on hyperbolic spaces $H_{κ}^{n}$ with curvature $- κ < 0$ . We prove the…

math.AP2021

System of Degenerate Parabolic $p$ -Laplacian

Sunghoon Kim, Ki-Ahm Lee

In this paper, we study the mathematical properties of the solution $u = (u^{1}, \dots, u^{k})$ to the degenerate parabolic system \begin{equation*} \bold{u}_t=\nabla\cd…

math.AP2021★ 1 cited

Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature

Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee

We establish the Krylov Safonov Harnack inequalities and Holder estimates for fully nonlinear nonlocal operators of non-divergence form on Riemannian manifolds with nonnegative sec…

math.AP2020★ 1 cited

Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations

Sunghan Kim, Ki-Ahm Lee

This article is concerned with uniform $C^{1, α}$ and $C^{1, 1}$ estimates in periodic homogenization of fully nonlinear elliptic equations. The analysis is based on the compactness…

math.AP2020★ 8 cited

Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders

Minhyun Kim, Ki-Ahm Lee

We establish the generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear elliptic equations with rough kernels of variable orders. In contrast to the fra…

math.AP2020

Optimal configuration and symmetry breaking phenomena in the composite membrane problem with fractional Laplacian

María del Mar González, Ki-Ahm Lee, Taehun Lee

We consider the following eigenvalue optimization in the composite membrane problem with fractional Laplacian: given a bounded domain $Ω \subset R^{n}$ , $α > 0$ and $0 < A < ∣Ω∣$ ,…

math.AP2020

Properties of Generalized Degenerate Parabolic Systems

Sunghoon Kim, Ki-Ahm Lee

In this paper, we consider the solution $u = (u^{1}, \dots, u^{k})$ of the generalized parabolic system \begin{equation*} \left(u^i\right)_t=\nabla\cdot\left(mU^{m-1}\ma…

math.AP2018★ 1 cited

System of Porous Medium Equations

Sunghoon Kim, Ki-Ahm Lee

We investigate the evolution of population density vector, $u = (u^{1}, \dots, u^{k})$ , of $k$ -species whose diffusion is controlled by its absolute value $\left|\bold{u…

math.AP2018★ 1 cited

The scalar curvature flow with a flat side

Hyo Seok Jang, Ki-Ahm Lee

We study the near-the-interface behavior of a compact convex scalar curvature flow with a flat side. Under suitable initial conditions on the flat side, we show that the interface…

math.AP2018★ 9 cited

Regularity for fully nonlinear integro-differential operators with kernels of variable orders

Minhyun Kim, Ki-Ahm Lee

We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian…

math.AP2018★ 2 cited

The Regularity Theory for the Double Obstacle Problem for Fully Nonlinear Operator

Ki-ahm Lee, Jinwan Park

In this paper, we prove the existence and uniqueness of $W^{2, p}$ ( $n < p < \infty$ ) solutions of a double obstacle problem with $C^{1, 1}$ obstacle functions. Moreover, we show the opt…

math.AP2018★ 20 cited

Boundary regularity for nonlocal operators with kernels of variable orders

Minhyun Kim, Panki Kim, Jaehun Lee +1

We study the boundary regularity of solutions of the Dirichlet problem for the nonlocal operator with a kernel of variable orders. Since the order of differentiability of the kerne…

math.AP2018

Local Continuity and Asymptotic Behaviour of Degenerate Parabolic Systems

Sunghoon Kim, Ki-Ahm Lee

We study the local Hölder continuity and the asymptotic behaviour of solution, $u = (u^{1}, \dots, u^{k})$ , of the degenerate system \begin{equation*} u^i_t=\nabla\cdot\left(m\,…

math.AP2018

Regularity Results of the Thin Obstacle Problem for the $p (x)$ -Laplacian

Sun-sig Byun, Ki-ahm Lee, Jehan Oh +1

We study thin obstacle problems involving the energy functional with $p (x)$ -growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin o…

math.AP2017

Higher Order Convergence Rates in Theory of Homogenization III: viscous Hamilton-Jacobi Equations

Sunghan Kim, Ki-Ahm Lee

In this paper, we establish the higher order convergence rates in periodic homogenization of viscous Hamilton-Jacobi equations, which is convex and grows quadratically in the gradi…

math.AP2017★ 1 cited

Nodal Sets for "Broken" Quasilinear PDEs

Sunghan Kim, Ki-Ahm Lee, Henrik Shahgholian

We study the local behavior of the nodal sets of the solutions to elliptic quasilinear equations with nonlinear conductivity part, \begin{equation*} \operatorname{div}(A_s(x,u)\nab…

On the uniqueness of energy-minimizing curves in constrained spaces

The Wiener criterion for fully nonlinear elliptic equations

The fractional p-Laplacian on hyperbolic spaces

Global regularity results for a class of singular/degenerate fully nonlinear elliptic equations

C^{1,α}-regularity for a class of degenerate/singular fully nonlinear elliptic equations

The Wiener criterion for nonlocal Dirichlet problems

Uniform Integrability in Periodic Homogenization of Fully Nonlinear Equations

Robust near-diagonal Green function estimates

Harnack inequality for fractional Laplacian-type operators on hyperbolic spaces

System of Degenerate Parabolic p-Laplacian

Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature

Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations

Generalized Evans--Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders

Optimal configuration and symmetry breaking phenomena in the composite membrane problem with fractional Laplacian

Properties of Generalized Degenerate Parabolic Systems

System of Porous Medium Equations

The scalar curvature flow with a flat side

Regularity for fully nonlinear integro-differential operators with kernels of variable orders

The Regularity Theory for the Double Obstacle Problem for Fully Nonlinear Operator

Boundary regularity for nonlocal operators with kernels of variable orders

Local Continuity and Asymptotic Behaviour of Degenerate Parabolic Systems

Regularity Results of the Thin Obstacle Problem for the p(x)-Laplacian

Higher Order Convergence Rates in Theory of Homogenization III: viscous Hamilton-Jacobi Equations

Nodal Sets for "Broken" Quasilinear PDEs

The fractional $p$ -Laplacian on hyperbolic spaces

System of Degenerate Parabolic $p$ -Laplacian

Regularity Results of the Thin Obstacle Problem for the $p (x)$ -Laplacian