An improved version of a spectral inequality by Payne
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918346583179264 |
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| author | Acampora, Paolo Cristoforoni, Emanuele Nitsch, Carlo Trombetti, Cristina |
| author_facet | Acampora, Paolo Cristoforoni, Emanuele Nitsch, Carlo Trombetti, Cristina |
| contents | A celebrated inequality by Payne relates the first eigenvalue of the Dirichlet Laplacian to the first eigenvalue of the buckling problem. Motivated by the goal of establishing a quantitative version of this inequality, we show that Payne's original estimate - which is not sharp - can in fact be improved. Our result provides a refined spectral bound and opens the way to further investigations into quantitative enhancements of classical inequalities in spectral theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_08631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An improved version of a spectral inequality by Payne Acampora, Paolo Cristoforoni, Emanuele Nitsch, Carlo Trombetti, Cristina Analysis of PDEs 35P15, 55J35, 31B30, 35B40 A celebrated inequality by Payne relates the first eigenvalue of the Dirichlet Laplacian to the first eigenvalue of the buckling problem. Motivated by the goal of establishing a quantitative version of this inequality, we show that Payne's original estimate - which is not sharp - can in fact be improved. Our result provides a refined spectral bound and opens the way to further investigations into quantitative enhancements of classical inequalities in spectral theory. |
| title | An improved version of a spectral inequality by Payne |
| topic | Analysis of PDEs 35P15, 55J35, 31B30, 35B40 |
| url | https://arxiv.org/abs/2507.08631 |