16 citations · 62 across the 39 of their papers we have counts for
19 papers · 1 filter
Asymptotic profile of solutions to the heat equation on thin plate with boundary heating
Eun-ho Lee, Woocheol Choi
In this section, we consider the heat equation on a plate with thickness h > 0 being heated by a heat source on upper and lower faces of the plate. We obtain an asymptotic profile…
Semi-classical limit of quantum free energy minimizers for the gravitational Hartree equation
Woocheol Choi, Younghun Hong, Jinmyoung Seok
For the gravitational Vlasov-Poisson equation, Guo and Rein constructed a class of classical isotropic states as minimizers of free energies (or energy-Casimir functionals) under m…
Asymptotic behavior of least energy solutions to the Lane-Emden system near the critical hyperbola
Woocheol Choi, Seunghyeok Kim
The Lane-Emden system is written as \begin{equation*} \begin{cases} -Δu = v^p &\text{in } Ω,\\ -Δv = u^q &\text{in } Ω,\\ u, v > 0 &\text{in } Ω,\\ u = v = 0 &\text{on } \partial Ω…
Uniqueness and symmetry of ground states for higher-order equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
We establish uniqueness and radial symmetry of ground states for higher-order nonlinear Schrödinger and Hartree equations whose higher-order differentials have small coefficients.…
On critical and supercritical pseudo-relativistic nonlinear Schrödinger equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
In this paper, we investigate existence and non-existence of a nontrivial solution to the pseudo-relativistic nonlinear Schrödinger equation $$\left( \sqrt{-c^2Δ+ m^2 c^4}-mc^2\rig…
Optimal convergence rate of nonrelativistic limit for the nonlinear pseudo-relativistic equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
In this paper, we are concerned with the nonrelativistic limit of the following pseudo-relativistic equation with Hartree nonlinearity or power type nonlinearity \[ \left(\sqrt{-\h…
Minimal energy solutions to the fractional Lane-Emden system, I: Existence and singularity formation
Woocheol Choi, Seunghyeok Kim
This is the first of two papers which study asymptotic behavior of minimal energy solutions to the fractional Lane-Emden system in a smooth bounded domain \[(-Δ)^s u = v^p, \qu…
On the splitting method for the nonlinear Schrödinger equation with initial data in
Woocheol Choi, Youngwoo Koh
In this paper, we establish a convergence result for the operator splitting scheme introduced by Ignat, with initial data in , for the nonlinear Schrödinger equation : $…
Semilinear elliptic equations with the pseudo-relativistic operator on a bounded domain
Woocheol Choi, Younghun Hong, Jinmyoung Seok
We study the Dirichlet problem for the semilinear equations involving the pseudo-relativistic operator on a bounded domain, (\sqrt{-Δ+ m^2} - m)u =|u|^{p-1}u \quad \textrm{in}~Ω, w…
Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents
Woocheol Choi, Seunghyeok Kim
We study qualitative properties of solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents where the associated fractional Laplacian is defined…
Nonrelativistic limit of standing waves for pseudo-relativistic nonlinear Schrödinger equations
Woocheol Choi, Jinmyoung Seok
In this paper we study standing waves for pseudo-relativistic nonlinear Schrödinger equations. In the first part we find ground state solutions. We also prove that they have one si…
The Lane-Emden system near the critical hyperbola on nonconvex domains
Woocheol Choi
In this paper we study the asymptotic behavior of minimal energy solutions to the Lane-Emden system and on bounded domains as the index approaches t…
On perturbations of the fractional Yamabe problem
Woocheol Choi, Seunghyeok Kim
The fractional Yamabe problem, proposed by González-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature…
Qualitative properties of multi-bubble solutions for nonlinear elliptic equations involving critical exponents
Woocheol Choi, Seunghyeok Kim, Ki-Ahm Lee
The objective of this paper is to obtain qualitative characteristics of multi-bubble solutions to the Lane-Emden-Fowler equations with slightly subcritical exponents given any dime…
Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings
Woocheol Choi, Jinmyoung Seok
In this paper, we study a class of semilinear nonlocal elliptic equations posed on settings without compact Sobolev embedding. More precisely, we prove the existence of infinitely…
Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian
Woocheol Choi, Seunghyeok Kim, Ki-Ahm Lee
In this paper we study the asymptotic behavior of least energy solutions and the existence of multiple bubbling solutions of nonlinear elliptic equations involving the fractional L…
On strongly indefinite systems involving the fractional Laplacian
Woocheol Choi
In this paper we study strongly indefinite systems involving the fractional Laplacian on bounded domains. We obtain existence and non-existence results, estimates of Gid…
Maximal multipliers on compact manifolds without boundary
Woocheol Choi
Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obt…
Maximal multiplier on Stratified groups
Woocheol Choi
In this paper, we prove Lp boundedness of maximal multipliers on stratified groups and maximal multipliers on product spaces of those groups.