2 citations · 3 across the 9 of their papers we have counts for
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Well-Posedness for Cauchy Problems with Singular Time-Measurable Pseudo-Differential Operators in Quasi-decreasing Weighted -Spaces
Jae-Hwan Choi, Ildoo Kim
This study examines Cauchy problems governed by highly singular, time-measurable pseudo-differential operators (singular measurable families of Fourier multipliers). We show that t…
An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity
Jae-Hwan Choi, Ildoo Kim
We broaden the domain of the Fourier transform to contain all distributions without using the Paley-Wiener theorem and devise a new weak formulation built upon this extension. This…
A regularity theory for parabolic equations with anisotropic non-local operators in spaces
Jae-Hwan Choi, Jaehoon Kang, Daehan Park
In this paper, we present an -regularity theory for parabolic equations of the form: …
A regularity theory for an initial value problem with a time-measurable pseudo-differential operator in a weighted -space
Jae-Hwan Choi, Ildoo Kim, Jin Bong Lee
In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differ…
A weighted -regularity theory for parabolic partial differential equations with time measurable pseudo-differential operators
Jae-Hwan Choi, Ildoo Kim
We obtain the existence, uniqueness, and regularity estimates of the following Cauchy problem \begin{equation}\label{ab eqn} \begin{cases} \partial_t u(t,x)=ψ(t,-i\nabla)u(t,x)+f(t…
Sobolev regularity theory for the non-local elliptic and parabolic equations on open sets
Jae-Hwan Choi, Kyeong-Hun Kim, Junhee Ryu
We study the zero exterior problem for the elliptic equation as well as for the parabolic equation $$ u_t=Δ^{α/2}u+f, \quad t>…