Year: 2025
Type: preprint
Abstract: 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 pointwise estimates in terms of the data in the spirit of nonlinear potential theory, leading to fine gradient regularity results under borderline assumptions on the data. Notably, our gradient estimates are novel already in the absence of forcing terms and even for linear kinetic Fokker-Planck equations in divergence form.
Source: arXiv (Cornell University)
Authors: Kim, Kyeongbae, Lee, Ho-Sik, Nowak, Simon
Institutions: Seoul National University, Bielefeld University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1288578048, G1658918567, G2442903552, GRK 2235: Das Reguläre im Irregulären: Analysis von singulären und zufälligen Systemen, G3054641961, G3883322829, G467907816, G8201362140, SFB 1283: Unsicherheit beherrschen und Zufall sowie Unordnung nutzen in Analysis, Stochastik und deren Anwendungen
OpenAlex ID: W4407576003