Estimates on the Neumann and Steklov principal eigenvalues of collapsing domains
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909521694162944 |
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| author | Acampora, Paolo Amato, Vincenzo Cristoforoni, Emanuele |
| author_facet | Acampora, Paolo Amato, Vincenzo Cristoforoni, Emanuele |
| contents | We investigate the relationship between the Neumann and Steklov principal eigenvalues emerging from the study of collapsing convex domains in $\mathbb{R}^2$. Such a relationship allows us to give a partial proof of a conjecture concerning estimates of the ratio of the former to the latter: we show that thinning triangles maximize the ratio among convex thinning sets, while thinning rectangles minimize the ratio among convex thinning with some symmetry property. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_12889 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Estimates on the Neumann and Steklov principal eigenvalues of collapsing domains Acampora, Paolo Amato, Vincenzo Cristoforoni, Emanuele Analysis of PDEs 35P15, 49Q10, 52A40 We investigate the relationship between the Neumann and Steklov principal eigenvalues emerging from the study of collapsing convex domains in $\mathbb{R}^2$. Such a relationship allows us to give a partial proof of a conjecture concerning estimates of the ratio of the former to the latter: we show that thinning triangles maximize the ratio among convex thinning sets, while thinning rectangles minimize the ratio among convex thinning with some symmetry property. |
| title | Estimates on the Neumann and Steklov principal eigenvalues of collapsing domains |
| topic | Analysis of PDEs 35P15, 49Q10, 52A40 |
| url | https://arxiv.org/abs/2307.12889 |