Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916234088415232 |
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| author | Anceschi, Francesca Ascione, Giacomo Castorina, Daniele Solombrino, Francesco |
| author_facet | Anceschi, Francesca Ascione, Giacomo Castorina, Daniele Solombrino, Francesco |
| contents | We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and uniqueness of measure solutions to the associated Cauchy problem, as well as the equivalence with the corresponding stochastic formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift Anceschi, Francesca Ascione, Giacomo Castorina, Daniele Solombrino, Francesco Analysis of PDEs 35Q84, 35A08, 60H10, 60H30 We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and uniqueness of measure solutions to the associated Cauchy problem, as well as the equivalence with the corresponding stochastic formulation. |
| title | Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift |
| topic | Analysis of PDEs 35Q84, 35A08, 60H10, 60H30 |
| url | https://arxiv.org/abs/2405.01955 |