6 papers · 1 filter
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…
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…
The De Giorgi method for local and nonlocal systems
Linus Behn, Lars Diening, Simon Nowak +1
We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application…
Potential theory for nonlocal drift-diffusion equations
Quoc-Hung Nguyen, Simon Nowak, Yannick Sire +1
The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assum…