On the kinetic $p$-Laplace equation with nonlocal diffusion
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913149339303936 |
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| author | Niebel, Lukas |
| author_facet | Niebel, Lukas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21080 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the kinetic $p$-Laplace equation with nonlocal diffusion Niebel, Lukas Analysis of PDEs 35H10, 35R09, 35K92 (Primary) 35Q49, 46E35, 35A30, 35A23 (Secondary) 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. |
| title | On the kinetic $p$-Laplace equation with nonlocal diffusion |
| topic | Analysis of PDEs 35H10, 35R09, 35K92 (Primary) 35Q49, 46E35, 35A30, 35A23 (Secondary) |
| url | https://arxiv.org/abs/2605.21080 |