Sobolev embeddings for kinetic Fokker-Planck equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914653542547456 |
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| author | Pascucci, Andrea Pesce, Antonello |
| author_facet | Pascucci, Andrea Pesce, Antonello |
| contents | We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak Hörmander condition. We prove continuous embeddings into Lorentz and intrinsic Hölder spaces. We also prove approximation and interpolation inequalities by means of an intrinsic Taylor expansion, extending analogous results for Hölder spaces. The embedding at first order is proved by adapting a method by Luc Tartar which only exploits scaling properties of the intrinsic quasi-norm, while for higher orders we use uniform kernel estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05124 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sobolev embeddings for kinetic Fokker-Planck equations Pascucci, Andrea Pesce, Antonello Analysis of PDEs Functional Analysis We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak Hörmander condition. We prove continuous embeddings into Lorentz and intrinsic Hölder spaces. We also prove approximation and interpolation inequalities by means of an intrinsic Taylor expansion, extending analogous results for Hölder spaces. The embedding at first order is proved by adapting a method by Luc Tartar which only exploits scaling properties of the intrinsic quasi-norm, while for higher orders we use uniform kernel estimates. |
| title | Sobolev embeddings for kinetic Fokker-Planck equations |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2209.05124 |