Nonlinear Kinetic Diffusion Equations with $p$-Growth
Analysis of PDEs
2026-05-19 v1
Abstract
We establish the local boundedness of (sub-)solutions to nonlinear kinetic diffusion equations with -growth, where the kinetic p-Laplace equation is a prototypical example. A key ingredient is the derivation of kinetic Gagliardo-Nirenberg inequalities, where the Lebesgue norm of a function is estimated in terms of its transport and diffusive directions controlled in different Lebesgue spaces.
Cite
@article{arxiv.2605.18521,
title = {Nonlinear Kinetic Diffusion Equations with $p$-Growth},
author = {Helge Dietert and Lukas Niebel and Rico Zacher},
journal= {arXiv preprint arXiv:2605.18521},
year = {2026}
}