Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866917840385212416 |
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| author | Frank, Rupert L. Helffer, Bernard Laptev, Ari |
| author_facet | Frank, Rupert L. Helffer, Bernard Laptev, Ari |
| contents | We show that the $j$-th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the $(j+1)$-st Neumann eigenvalue. This extends earlier results in the Euclidean and Heisenberg case and has a remarkably simple proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups Frank, Rupert L. Helffer, Bernard Laptev, Ari Analysis of PDEs Spectral Theory We show that the $j$-th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the $(j+1)$-st Neumann eigenvalue. This extends earlier results in the Euclidean and Heisenberg case and has a remarkably simple proof. |
| title | Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2411.11168 |