Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915662741372928 |
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| author | Auscher, Pascal Imbert, Cyril Niebel, Lukas |
| author_facet | Auscher, Pascal Imbert, Cyril Niebel, Lukas |
| contents | We prove existence, uniqueness and regularity of weak solutions of Kolmogorov--Fokker--Planck equations with either local or non-local diffusion in the velocity variable and rough diffusion coefficients or kernels. Our results cover the Cauchy problem and allow a broad class of source terms under minimal assumptions. The core of the analysis is a set of sharp kinetic embeddings à la Lions and transfer-of-regularity results à la Bouchut--H\''ormander. We formulate these tools in a homogeneous, scale-invariant form, available for a large range of regularity parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness Auscher, Pascal Imbert, Cyril Niebel, Lukas Analysis of PDEs We prove existence, uniqueness and regularity of weak solutions of Kolmogorov--Fokker--Planck equations with either local or non-local diffusion in the velocity variable and rough diffusion coefficients or kernels. Our results cover the Cauchy problem and allow a broad class of source terms under minimal assumptions. The core of the analysis is a set of sharp kinetic embeddings à la Lions and transfer-of-regularity results à la Bouchut--H\''ormander. We formulate these tools in a homogeneous, scale-invariant form, available for a large range of regularity parameters. |
| title | Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.17464 |