Solvability of Vekua-type periodic operators and applications to classical equations
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910360559157248 |
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| author | Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer |
| author_facet | Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer |
| contents | In this note, we investigate Vekua-type periodic operators of the form $Pu=Lu-Au-B\bar u$, where $L$ is a constant coefficient partial differential operator. We provide a complete characterization of the necessary and sufficient conditions for the solvability and global hypoellipticity of $P$. As an application, we provide a comprehensive characterization of Vekua-type operators associated with classical wave, heat, and Laplace equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_10683 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solvability of Vekua-type periodic operators and applications to classical equations Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer Analysis of PDEs Primary 35B10 Secondary 35E20, 30G20 In this note, we investigate Vekua-type periodic operators of the form $Pu=Lu-Au-B\bar u$, where $L$ is a constant coefficient partial differential operator. We provide a complete characterization of the necessary and sufficient conditions for the solvability and global hypoellipticity of $P$. As an application, we provide a comprehensive characterization of Vekua-type operators associated with classical wave, heat, and Laplace equations. |
| title | Solvability of Vekua-type periodic operators and applications to classical equations |
| topic | Analysis of PDEs Primary 35B10 Secondary 35E20, 30G20 |
| url | https://arxiv.org/abs/2311.10683 |