On the Sobolev boundedness of vector fields on compact Riemannian manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908413833773056 |
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| author | Cardona, Duván Kirilov, Alexandre de Moraes, Wagner A. A. Kowacs, André Pedroso |
| author_facet | Cardona, Duván Kirilov, Alexandre de Moraes, Wagner A. A. Kowacs, André Pedroso |
| contents | We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of eigenvalues associated with these vector fields. As an application, we demonstrate the ill-posedness of a class of Cauchy problems involving left-invariant vector fields on compact Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Sobolev boundedness of vector fields on compact Riemannian manifolds Cardona, Duván Kirilov, Alexandre de Moraes, Wagner A. A. Kowacs, André Pedroso Analysis of PDEs We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of eigenvalues associated with these vector fields. As an application, we demonstrate the ill-posedness of a class of Cauchy problems involving left-invariant vector fields on compact Lie groups. |
| title | On the Sobolev boundedness of vector fields on compact Riemannian manifolds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.00182 |