A regularity theory for an initial value problem with a time-measurable pseudo-differential operator in a weighted -space

JH Choi, I Kim, JB Lee - arXiv preprint arXiv:2302.07507, 2023 - arxiv.org
We study initial value problems with (time-measurable) pseudo-differential operators in
weighted $ L_p $-spaces. Initial data are given in generalized Besov spaces and regularity …

An Lq (Lp)-regularity theory for parabolic equations with integro-differential operators having low intensity kernels

J Kang, D Park - Journal of Differential Equations, 2025 - Elsevier
In this article, we present the existence, uniqueness, and regularity of solutions to parabolic
equations with non-local operators∂ tu (t, x)= L au (t, x)+ f (t, x), t> 0 in L q (L p) spaces. Our …

A regularity theory for evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces

JH Choi - arXiv preprint arXiv:2402.03609, 2024 - arxiv.org
arXiv:2402.03609v1 [math.AP] 6 Feb 2024 Page 1 arXiv:2402.03609v1 [math.AP] 6 Feb 2024
A REGULARITY THEORY FOR EVOLUTION EQUATIONS WITH TIME-MEASURABLE …

An existence and uniqueness theory to stochastic partial differential equations involving pseudo-differential operators driven by space-time white noise

JH Choi, I Kim - arXiv preprint arXiv:2408.04529, 2024 - arxiv.org
In this paper, we aim to develop a new weak formulation that ensures well-posedness for a
broad range of stochastic partial differential equations with pseudo-differential operators …

An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators …

JH Choi, I Kim - arXiv preprint arXiv:2403.19968, 2024 - arxiv.org
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 weighted -theory for fully degenerate second-order evolution equations with unbounded time-measurable coefficients

I Kim - Stochastics and Partial Differential Equations: Analysis …, 2024 - Springer
We study the fully degenerate second-order evolution equation 0.1 ut= a ij (t) uxixj+ bi (t)
uxi+ c (t) u+ f, t> 0, x∈ R d given with the zero initial data. Here a ij (t), bi (t), c (t) are merely …