On the kinetic $p$-Laplace equation with nonlocal diffusion

Lukas Niebel

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arXiv · 2605.21080

On the kinetic $p$-Laplace equation with nonlocal diffusion

Lukas Niebel

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Abstract

We study two nonlocal versions of the kinetic $p$-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 $p$-Laplace equations with nonlocal diffusion.

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Lukas Niebel. 2026-05-20. On the kinetic $p$-Laplace equation with nonlocal diffusion. https://arxiv.org/abs/2605.21080

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