Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918058785767424 |
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| author | Silva, Fernando de Ávila Cappiello, Marco Kirilov, Alexandre |
| author_facet | Silva, Fernando de Ávila Cappiello, Marco Kirilov, Alexandre |
| contents | We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and sufficient conditions for the global hypoellipticity of this class of systems, stated in terms of Diophantine-type estimates and sign-changing behavior of the imaginary parts of the coefficients. Through a reduction to a normal form and detailed construction of singular solutions, we fully characterize when the system fails to be globally hypoelliptic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12178 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces Silva, Fernando de Ávila Cappiello, Marco Kirilov, Alexandre Analysis of PDEs 35H10, 35N10, 35B10, 46F05 We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and sufficient conditions for the global hypoellipticity of this class of systems, stated in terms of Diophantine-type estimates and sign-changing behavior of the imaginary parts of the coefficients. Through a reduction to a normal form and detailed construction of singular solutions, we fully characterize when the system fails to be globally hypoelliptic. |
| title | Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces |
| topic | Analysis of PDEs 35H10, 35N10, 35B10, 46F05 |
| url | https://arxiv.org/abs/2506.12178 |