Kinetic maximal $L^2$-regularity for the (fractional) Kolmogorov equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866912660971323392 |
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| author | Niebel, Lukas Zacher, Rico |
| author_facet | Niebel, Lukas Zacher, Rico |
| contents | We introduce the notion of kinetic maximal $L^2$-regularity with temporal weights for the (fractional) Kolmogorov equation. In particular, we determine the function spaces for the inhomogeneity and the initial value which characterize the regularity of solutions to the fractional Kolmogorov equation in terms of fractional anisotropic Sobolev spaces. It is shown that solutions of the homogeneous (fractional) Kolmogorov equation define a semi-flow in a suitable function space and the property of instantaneous regularization is investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_11531 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Kinetic maximal $L^2$-regularity for the (fractional) Kolmogorov equation Niebel, Lukas Zacher, Rico Analysis of PDEs 35K65, 35B65, 35H10 We introduce the notion of kinetic maximal $L^2$-regularity with temporal weights for the (fractional) Kolmogorov equation. In particular, we determine the function spaces for the inhomogeneity and the initial value which characterize the regularity of solutions to the fractional Kolmogorov equation in terms of fractional anisotropic Sobolev spaces. It is shown that solutions of the homogeneous (fractional) Kolmogorov equation define a semi-flow in a suitable function space and the property of instantaneous regularization is investigated. |
| title | Kinetic maximal $L^2$-regularity for the (fractional) Kolmogorov equation |
| topic | Analysis of PDEs 35K65, 35B65, 35H10 |
| url | https://arxiv.org/abs/2006.11531 |