On the kinetic $p$-Laplace equation with nonlocal diffusion
Analysis of PDEs
2026-05-21 v1
Abstract
We study two nonlocal versions of the kinetic -Laplace equation: a Gagliardo-type model defined through differences and a Bessel-type model defined via Fourier multiplication. Using critical kinetic trajectories, we derive representation formulas adapted to the kinetic transport-diffusion geometry and establish homogeneous and scale-invariant kinetic Gagliardo-Nirenberg inequalities for nonlocal diffusion, which yield gain-of-integrability estimates for weak solutions to the kinetic -Laplace equations with nonlocal diffusion.
Keywords
Cite
@article{arxiv.2605.21080,
title = {On the kinetic $p$-Laplace equation with nonlocal diffusion},
author = {Lukas Niebel},
journal= {arXiv preprint arXiv:2605.21080},
year = {2026}
}