Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916883506135040 |
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| author | Anceschi, Francesca Dietert, Helge Guerand, Jessica Loher, Amélie Mouhot, Clément Rebucci, Annalaura |
| author_facet | Anceschi, Francesca Dietert, Helge Guerand, Jessica Loher, Amélie Mouhot, Clément Rebucci, Annalaura |
| contents | We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörmander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak Harnack inequality and Hölder regularity along the line of the De Giorgi method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators Anceschi, Francesca Dietert, Helge Guerand, Jessica Loher, Amélie Mouhot, Clément Rebucci, Annalaura Analysis of PDEs 35K70, 35H10, 35B65, 35B45, 35A23 We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörmander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak Harnack inequality and Hölder regularity along the line of the De Giorgi method. |
| title | Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators |
| topic | Analysis of PDEs 35K70, 35H10, 35B65, 35B45, 35A23 |
| url | https://arxiv.org/abs/2401.12194 |