Global hypoellipticity for a class of complex-valued evolution equations on compact Lie groups
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918076576956416 |
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| author | de Moraes, Wagner A. A. |
| author_facet | de Moraes, Wagner A. A. |
| contents | We present necessary and sufficient conditions to have global hypoellipticity for a class of complex-valued coefficient first order evolution equations defined on $\mathbb{T}^1 \times G$, where $G$ is a compact Lie group. First, we show that the global hypoellipticity of the constant coefficient operator related to this operator is a necessary condition, but not a sufficient condition. Under certain hypothesis, we show that the global hypoellipticity of this class of operator is completely characterized by Nirenberg-Treves' condition $(\mathcal{P})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global hypoellipticity for a class of complex-valued evolution equations on compact Lie groups de Moraes, Wagner A. A. Analysis of PDEs Primary 35F05, 58D25, Secondary 35B10, 43A77 We present necessary and sufficient conditions to have global hypoellipticity for a class of complex-valued coefficient first order evolution equations defined on $\mathbb{T}^1 \times G$, where $G$ is a compact Lie group. First, we show that the global hypoellipticity of the constant coefficient operator related to this operator is a necessary condition, but not a sufficient condition. Under certain hypothesis, we show that the global hypoellipticity of this class of operator is completely characterized by Nirenberg-Treves' condition $(\mathcal{P})$. |
| title | Global hypoellipticity for a class of complex-valued evolution equations on compact Lie groups |
| topic | Analysis of PDEs Primary 35F05, 58D25, Secondary 35B10, 43A77 |
| url | https://arxiv.org/abs/2402.04950 |