Global Solvability for Involutive Systems on Non-Compact Manifolds
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915643033387008 |
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| author | Coriasco, Sandro Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer |
| author_facet | Coriasco, Sandro Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer |
| contents | We establish necessary and sufficient conditions for the closedness of the range of a class of first-order differential operators associated with an involutive structure on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold satisfying suitable geometric assumptions and $\mathbb{T}^m$ is the $m$-dimensional torus. In addition, we prove that a weaker notion of global hypoellipticity ensures the closedness of the range for differential operators on smooth paracompact manifolds, thereby extending to the non-compact setting a result previously obtained by G.~Araújo, I.~Ferra, and L.~Ragognette [J. Anal. Math. 148, No. 1, 85-118, 2022] for compact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Solvability for Involutive Systems on Non-Compact Manifolds Coriasco, Sandro Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer Analysis of PDEs Primary 35N10, 58J10, Secondary 35B65, 58J40 We establish necessary and sufficient conditions for the closedness of the range of a class of first-order differential operators associated with an involutive structure on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold satisfying suitable geometric assumptions and $\mathbb{T}^m$ is the $m$-dimensional torus. In addition, we prove that a weaker notion of global hypoellipticity ensures the closedness of the range for differential operators on smooth paracompact manifolds, thereby extending to the non-compact setting a result previously obtained by G.~Araújo, I.~Ferra, and L.~Ragognette [J. Anal. Math. 148, No. 1, 85-118, 2022] for compact manifolds. |
| title | Global Solvability for Involutive Systems on Non-Compact Manifolds |
| topic | Analysis of PDEs Primary 35N10, 58J10, Secondary 35B65, 58J40 |
| url | https://arxiv.org/abs/2511.22741 |