The Buckling and Clamped Plate Problems on Differential Forms
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917246101618688 |
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| author | Chami, Fida El Ginoux, Nicolas Habib, Georges Makhoul, Ola Raulot, Simon |
| author_facet | Chami, Fida El Ginoux, Nicolas Habib, Georges Makhoul, Ola Raulot, Simon |
| contents | We extend the buckling and clamped-plate problems to the context of differential forms on compact Riemannian manifolds with smooth boundary. We characterize their smallest eigenvalues and prove that, in the case of bounded Euclidean domains, their spectra without multiplicities on forms coincide with the spectra of the corresponding problems on functions. We obtain various estimates involving the first eigenvalues of the mentioned problems and the ones of the Hodge Laplacian with respect to Dirichlet and absolute boundary conditions on forms. These estimates generalize previous ones in the case of functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Buckling and Clamped Plate Problems on Differential Forms Chami, Fida El Ginoux, Nicolas Habib, Georges Makhoul, Ola Raulot, Simon Differential Geometry Analysis of PDEs Spectral Theory 53C21, 58J32, 58C40, 58J50 We extend the buckling and clamped-plate problems to the context of differential forms on compact Riemannian manifolds with smooth boundary. We characterize their smallest eigenvalues and prove that, in the case of bounded Euclidean domains, their spectra without multiplicities on forms coincide with the spectra of the corresponding problems on functions. We obtain various estimates involving the first eigenvalues of the mentioned problems and the ones of the Hodge Laplacian with respect to Dirichlet and absolute boundary conditions on forms. These estimates generalize previous ones in the case of functions. |
| title | The Buckling and Clamped Plate Problems on Differential Forms |
| topic | Differential Geometry Analysis of PDEs Spectral Theory 53C21, 58J32, 58C40, 58J50 |
| url | https://arxiv.org/abs/2412.05612 |