16 citations · 28 across the 4 of their papers we have counts for
5 papers
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 -theory () for the time-fractional quasi-linear stochastic partial differential equations (SPDEs) of type $$ \partial^α_tu=L(ω,t,x)u+f(u…
An -theory for the time fractional evolution equations with variable coefficients
Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim
We introduce an -theory for the quasi-linear fractional equations of the type $$ \partial^α_t u(t,x)=a^{ij}(t,x)u_{x^i x^j}(t,x)+f(t,x,u), \quad t>0, \,x\in \mathbf{R}^d.…
Asymptotic behaviors of fundamental solution and its derivatives related to space-time fractional differential equations
Kyeong-Hun Kim, Sungbin Lim
Let be the fundamental solution to the problem In this paper we provide the asymptotic behaviors and…
An -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 of arbitrary order $γ\in(0,\infty)…
Parabolic Littlewood-Paley inequality for a class of time-dependent operators of arbitrary order, and applications to higher order stochastic PDE
Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim
In this paper we prove a parabolic version of the Littlewood-Paley inequality for a class of time-dependent local and non-local operators of arbitrary order, and as an application…