Kinetic maximal $L^p_μ(L^p)$-regularity for the fractional Kolmogorov equation with variable density
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866908603768635392 |
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| author | Niebel, Lukas |
| author_facet | Niebel, Lukas |
| contents | We consider the Kolmogorov equation, where the right-hand side is given by a non-local integro-differential operator comparable to the fractional Laplacian in velocity with possibly time, space and velocity dependent density. We prove that this equation admits kinetic maximal $L^p_μ$-regularity under suitable assumptions on the density and on $p$ and $μ$. We apply this result to prove short-time existence of strong $L^p_μ$-solutions to quasilinear fractional kinetic partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_05966 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Kinetic maximal $L^p_μ(L^p)$-regularity for the fractional Kolmogorov equation with variable density Niebel, Lukas Analysis of PDEs 35K59, 35K65, 45K05 We consider the Kolmogorov equation, where the right-hand side is given by a non-local integro-differential operator comparable to the fractional Laplacian in velocity with possibly time, space and velocity dependent density. We prove that this equation admits kinetic maximal $L^p_μ$-regularity under suitable assumptions on the density and on $p$ and $μ$. We apply this result to prove short-time existence of strong $L^p_μ$-solutions to quasilinear fractional kinetic partial differential equations. |
| title | Kinetic maximal $L^p_μ(L^p)$-regularity for the fractional Kolmogorov equation with variable density |
| topic | Analysis of PDEs 35K59, 35K65, 45K05 |
| url | https://arxiv.org/abs/2103.05966 |