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math.AP2025
Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem
Kyeongbae Kim, Ho-Sik Lee, Harsh Prasad
We establish certain oscillation estimates for weak solutions to nonlinear, anomalous phase transitions modeled on the nonlocal two-phase Stefan problem. The problem is singular in…
math.AP2025
Local Hölder Regularity For Nonlocal Porous Media And Fast Diffusion Equations With General Kernel
Kyeongbae Kim, Ho-Sik Lee, Harsh Prasad
We show that locally bounded, local weak solutions to certain nonlocal, nonlinear diffusion equations modeled on the fractional porous media and fast diffusion equations given by \…
math.AP2025
Gradient estimates for nonlinear kinetic Fokker-Planck equations
Kyeongbae Kim, Ho-Sik Lee, Simon Nowak
In this work, we provide a comprehensive gradient regularity theory for a broad class of nonlinear kinetic Fokker-Planck equations. We achieve this by establishing precise pointwis…