The Harnack inequality fails for nonlocal kinetic equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910683108474880 |
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| author | Kassmann, Moritz Weidner, Marvin |
| author_facet | Kassmann, Moritz Weidner, Marvin |
| contents | We prove that the Harnack inequality fails for nonlocal kinetic equations. Such equations arise as linearized models for the Boltzmann equation without cutoff and are of hypoelliptic type. We provide a counterexample for the simplest equation in this theory, the fractional Kolmogorov equation. Our result reflects a purely nonlocal phenomenon since the Harnack inequality holds true for local kinetic equations like the Kolmogorov equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05223 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Harnack inequality fails for nonlocal kinetic equations Kassmann, Moritz Weidner, Marvin Analysis of PDEs Probability 47G20, 35B65, 35R09, 35H10, 31B05, 35Q20, 82C40 We prove that the Harnack inequality fails for nonlocal kinetic equations. Such equations arise as linearized models for the Boltzmann equation without cutoff and are of hypoelliptic type. We provide a counterexample for the simplest equation in this theory, the fractional Kolmogorov equation. Our result reflects a purely nonlocal phenomenon since the Harnack inequality holds true for local kinetic equations like the Kolmogorov equation. |
| title | The Harnack inequality fails for nonlocal kinetic equations |
| topic | Analysis of PDEs Probability 47G20, 35B65, 35R09, 35H10, 31B05, 35Q20, 82C40 |
| url | https://arxiv.org/abs/2405.05223 |