On the optimal sets in Pólya and Makai type inequalities
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910027339530240 |
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| author | Amato, Vincenzo Gavitone, Nunzia Sannipoli, Rossano |
| author_facet | Amato, Vincenzo Gavitone, Nunzia Sannipoli, Rossano |
| contents | In this paper, we examine some shape functionals, introduced by Pólya and Makai, involving the torsional rigidity and the first Dirichlet-Laplacian eigenvalue for bounded, open and convex sets of $\mathbb{R}^n$. We establish new quantitative bounds, which give us key properties and information on the behavior of the optimizing sequences. In particular, we consider two kinds of reminder terms that provide information about the structure of these minimizing sequences, such as information about the thickness. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_06858 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the optimal sets in Pólya and Makai type inequalities Amato, Vincenzo Gavitone, Nunzia Sannipoli, Rossano Analysis of PDEs Spectral Theory 35P15, 49Q10, 35J05, 35J25 In this paper, we examine some shape functionals, introduced by Pólya and Makai, involving the torsional rigidity and the first Dirichlet-Laplacian eigenvalue for bounded, open and convex sets of $\mathbb{R}^n$. We establish new quantitative bounds, which give us key properties and information on the behavior of the optimizing sequences. In particular, we consider two kinds of reminder terms that provide information about the structure of these minimizing sequences, such as information about the thickness. |
| title | On the optimal sets in Pólya and Makai type inequalities |
| topic | Analysis of PDEs Spectral Theory 35P15, 49Q10, 35J05, 35J25 |
| url | https://arxiv.org/abs/2410.06858 |