Relations between different types of Hypoellipticity: A systematic approach
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909614476361728 |
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| author | Victor, Bruno de Lessa Ragognette, Luis F. |
| author_facet | Victor, Bruno de Lessa Ragognette, Luis F. |
| contents | We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity implies another one and, in particular, when it can be extended for more general spaces. We also present a relation between certain types of hypoellipticity and local solvability (for the transpose) for a family of operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relations between different types of Hypoellipticity: A systematic approach Victor, Bruno de Lessa Ragognette, Luis F. Analysis of PDEs Functional Analysis 35H10 (primary), 35B65, 35A09 (secondary) We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity implies another one and, in particular, when it can be extended for more general spaces. We also present a relation between certain types of hypoellipticity and local solvability (for the transpose) for a family of operators. |
| title | Relations between different types of Hypoellipticity: A systematic approach |
| topic | Analysis of PDEs Functional Analysis 35H10 (primary), 35B65, 35A09 (secondary) |
| url | https://arxiv.org/abs/2505.11801 |