Global hypoellipticity for involutive systems on non-compact manifolds
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908678034030592 |
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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 study the global hypoellipticity of the operator $\mathbb{L} = \mathrm{d}_t + \sum_{k=1}^m ω_k \wedge \partial_{x_k}$, defined on differential forms over product manifolds of the form $M \times \mathbb{T}^m$, where $M$ is a non-compact manifold homeomorphic to the interior of a compact manifold with boundary, equipped with a scattering metric, and $ω_1,\dots,ω_m$ are smooth closed 1-forms on $M$. Extending previous results obtained in the compact setting, we characterize global hypoellipticity of $\mathbb{L}$ in terms of arithmetic properties of the forms $ω_k$. The analysis relies on microlocal techniques adapted to the scattering setting and a version of the Hodge Theorem for scattering manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global hypoellipticity 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 study the global hypoellipticity of the operator $\mathbb{L} = \mathrm{d}_t + \sum_{k=1}^m ω_k \wedge \partial_{x_k}$, defined on differential forms over product manifolds of the form $M \times \mathbb{T}^m$, where $M$ is a non-compact manifold homeomorphic to the interior of a compact manifold with boundary, equipped with a scattering metric, and $ω_1,\dots,ω_m$ are smooth closed 1-forms on $M$. Extending previous results obtained in the compact setting, we characterize global hypoellipticity of $\mathbb{L}$ in terms of arithmetic properties of the forms $ω_k$. The analysis relies on microlocal techniques adapted to the scattering setting and a version of the Hodge Theorem for scattering manifolds. |
| title | Global hypoellipticity for involutive systems on non-compact manifolds |
| topic | Analysis of PDEs Primary 35N10, 58J10, Secondary 35B65, 58J40 |
| url | https://arxiv.org/abs/2505.01889 |