KyeongRo Kim

activity

20112026

most citedAsymptotic behaviors of fundamental solution and its derivatives related to space-time fractional differential equations

16 citations · 31 across the 14 of their papers we have counts for

collaborators

15 papers

math.AP2026

The Neumann problem for stochastic partial differential equations

Kyeong-Hun Kim, Junhee Ryu

In this paper, we study the Neumann problem for second-order stochastic partial differential equations in the half space. The coefficients are random and merely measurable in time.…

math.AP2023

Weighted Sobolev space theory for non-local elliptic and parabolic equations with non-zero exterior condition on $C^{1, 1}$ open sets

Kyeong-Hun Kim, Junhee Ryu

We introduce a weighted Sobolev space theory for the non-local elliptic equation $Δ^{α /2} u = f, x \in O; r_{O^{c}} u = g$ as well as for th…

math.AP2022

Sobolev regularity theory for the non-local elliptic and parabolic equations on $C^{1, 1}$ open sets

Jae-Hwan Choi, Kyeong-Hun Kim, Junhee Ryu

We study the zero exterior problem for the elliptic equation $Δ^{α /2} u - λ u = f, x \in D; u ∣_{D^{c}} = 0$ as well as for the parabolic equation $$ u_t=Δ^{α/2}u+f, \quad t>…

math.PR2021★ 2 cited

A Sobolev space theory for the Stochastic Partial Differential Equations with space-time non-local operators

Kyeong-Hun Kim, Daehan Park, Junhee Ryu

We deal with the Sobolev space theory for the stochastic partial differential equation (SPDE) driven by Wiener processes $$ \partial_{t}^αu=\left( ϕ(Δ) u +f(u) \right) + \partial_t…

math.AP2020★ 1 cited

An $L_{q} (L_{p})$ -theory for diffusion equations with space-time nonlocal operators

Kyeong-hun Kim, Daehan Park, Junhee Ryu

We present an $L_{q} (L_{p})$ -theory for the equation $\partial_{t}^{α} u = ϕ (Δ) u + f, t > 0, x \in R^{d}; u (0, \cdot) = u_{0} .$ Here $p, q > 1$ , $α \in (0, 1)$ , $\partial…

math.GT2020

A sequence of algebraic integer relation numbers which converges to 4

Wonyong Jang, KyeongRo Kim

Let $α \in R$ and let $A = [1011] and B_{α} = [1 α 01] .$ The subgroup $G_{α}$ of $\mathrm{SL}_…

math.GT2019

Laminar groups and 3-manifolds

Hyungryul Baik, KyeongRo Kim

Thurston showed that the fundamental group of a close atoroidal 3-manifold admitting a co-oriented taut foliation acts faithfully on the circle by orientation-preserving homeomorph…

math.AP2019★ 2 cited

Weighted $L_{q} (L_{p})$ -estimate with Muckenhoupt weights for the diffusion-wave equations with time-fractional derivatives

Beom-Seok Han, Kyeong-Hun Kim, Daehan Park

We present a weighted $L_{q} (L_{p})$ -theory ( $p, q \in (1, \infty)$ ) with Muckenhoupt weights for the equation $\partial_{t}^{α} u (t, x) = Δ u (t, x) + f (t, x), t > 0, x \in R^{d} .$ …

math.PR2019★ 4 cited

Boundary behavior and interior Hölder regularity of solution to nonlinear stochastic partial differential equations driven by space-time white noise

Beom-seok Han, Kyeong-hun Kim

We present uniqueness and existence in weighted Sobolev spaces of the equation $u_{t} = (a u_{xx} + b u_{x} + c u) + ξ ∣ u ∣^{1 + λ} B ˙, t > 0, x \in (0, 1)$ with initial data $u(…

math.PR2019★ 1 cited

A sharp $L_{p}$ -regularity result for second-order stochastic partial differential equations with unbounded and fully degenerate leading coefficients

Ildoo Kim, Kyeong-hun Kim

We present existence, uniqueness, and sharp regularity results of solution to the stochastic partial differential equation (SPDE) \begin{align} \label{abs eqn} du=(a^{ij}(ω,t)u_{x^…

math.AP2017

On the second order derivative estimates for degenerate parabolic equations

Ildoo Kim, Kyeong-hun Kim

We study the parabolic equation \begin{align} \notag &u_t(t,x)=a^{ij}(t)u_{x^ix^j}(t,x)+f(t,x), \quad (t,x) \in [0,T] \times \mathbf{R}^d \\ &u(0,x)=u_0(x) \label{main eqn} \end{al…

math.PR2016★ 1 cited

A Sobolev Space theory for stochastic partial differential equations with time-fractional derivatives

Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim

In this article we present an $L_{p}$ -theory ( $p \geq 2$ ) for the time-fractional quasi-linear stochastic partial differential equations (SPDEs) of type $$ \partial^α_tu=L(ω,t,x)u+f(u…

math.AP2015★ 16 cited

Asymptotic behaviors of fundamental solution and its derivatives related to space-time fractional differential equations

Kyeong-Hun Kim, Sungbin Lim

Let $p (t, x)$ be the fundamental solution to the problem $\partial_{t}^{α} u = - (- Δ)^{β} u, α \in (0, 2), β \in (0, \infty) .$ In this paper we provide the asymptotic behaviors and…

math.AP2015★ 3 cited

An $L_{q} (L_{p})$ -theory for parabolic pseudo-differential equations: Calderón-Zygmund approach

Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim

In this paper we present a Calderón-Zygmund approach for a large class of parabolic equations with pseudo-differential operators $A (t)$ of arbitrary order $γ\in(0,\infty)…

math.PR2011★ 1 cited

A weighted Sobolev space theory of parabolic stochastic PDEs on non-smooth domains

Kyeong-Hun Kim

In this paper we study parabolic stochastic partial differential equations defined on arbitrary bounded domain $\cO \subset \bR^d$ allowing Hardy inequality: $$ \int_{\cO}|ρ^{-1}g|…