5 papers · 2 filters
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…