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math.AP2025
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…
math.AP2025
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…
math.AP2024
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: …