11 papers
Kinetic Fokker-Planck equations with Maxwell boundary conditions
Kyeongbae Kim, Marvin Weidner
We develop the boundary regularity theory for solutions to linear kinetic Fokker-Planck equations with Maxwell boundary conditions. These conditions interpolate between diffuse and…
Boundary Harnack estimates of optimal order for kinetic Fokker-Planck equations
Kyeongbae Kim, Marvin Weidner
We establish higher order boundary Harnack estimates for solutions to kinetic Fokker-Planck equations with absorbing incoming boundaries. Unlike classical elliptic and parabolic eq…
Well-Posedness Of Second-Order Evolution Equations With Non-Integrable And Degenerate Coefficients In Weighted Lp-Spaces
Ildoo Kim, Kyeong-Hun Kim
We study the Cauchy problem for inhomogeneous evolution equations with time-dependent, potentially degenerate, and unbounded coefficients. A key feature of our work is allowing the…
Sharp regularity near the grazing set for kinetic Fokker-Planck equations
Kyeongbae Kim, Marvin Weidner
We prove optimal regularity results for solutions to linear kinetic Fokker-Planck equations in bounded domains. Our contributions are two-fold. First, we establish the sharp $C^{1/…
Fine regularity of fractional harmonic maps and applications
Kyeongbae Kim, Simon Nowak, Yannick Sire
In this paper, we derive several regularity results for harmonic mappings into Euclidean spheres associated with rather general energies related to fractional Sobolev spaces. These…
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…
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 \…
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…
Gradient estimates for parabolic nonlinear nonlocal equations
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
The primary objective of this work is to establish pointwise gradient estimates for solutions to a class of parabolic nonlinear nonlocal measure data problems, expressed in terms o…
Higher differentiability for the fractional -Laplacian
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
In this work, we study the higher differentiability of solutions to the inhomogeneous fractional -Laplace equation under different regularity assumptions on the data. In the sup…
Nonlinear nonlocal potential theory at the gradient level
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
The aim of this work is to establish numerous interrelated gradient estimates in the nonlinear nonlocal setting. First of all, we prove that weak solutions to a class of homogeneou…