Quantitative De Giorgi methods in kinetic theory for non-local operators
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929201407328256 |
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| author | Loher, Amélie |
| author_facet | Loher, Amélie |
| contents | We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies Hölder continuity. Our method is based on trajectories and exploits a term arising due to the non-locality in the energy estimate. This permits to quantitatively prove the intermediate value lemma for the full range of non-locality parameter $s \in (0, 1)$. Our results recover the results from Imbert and Silvestre [22] for the inhomogeneous Boltzmann equation in the non-cutoff case. The paper is self-contained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_16137 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantitative De Giorgi methods in kinetic theory for non-local operators Loher, Amélie Analysis of PDEs 45K05, 35Q20, 82C40, 35K99 We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies Hölder continuity. Our method is based on trajectories and exploits a term arising due to the non-locality in the energy estimate. This permits to quantitatively prove the intermediate value lemma for the full range of non-locality parameter $s \in (0, 1)$. Our results recover the results from Imbert and Silvestre [22] for the inhomogeneous Boltzmann equation in the non-cutoff case. The paper is self-contained. |
| title | Quantitative De Giorgi methods in kinetic theory for non-local operators |
| topic | Analysis of PDEs 45K05, 35Q20, 82C40, 35K99 |
| url | https://arxiv.org/abs/2203.16137 |