On some functionals involving torsional rigidity, principal eigenvalue and perimeter
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917203934183424 |
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| author | Amato, Vincenzo Nitsch, Carlo Trombetti, Cristina Villone, Federico |
| author_facet | Amato, Vincenzo Nitsch, Carlo Trombetti, Cristina Villone, Federico |
| contents | In this paper we study some relationships between the first Dirichlet eigenvalue $Λ(Ω)$ and the torsional rigidity $T(Ω)$ of a domain $Ω$. We consider the problem of optimizing the product $Λ(Ω)T(Ω)$ among sets with prescribed perimeter, both in the class of open sets with finite perimeter and within the class of convex domains.
We also present local results for the quantity $Λ(Ω)T(Ω)^q$, with $q>0$, under either a volume or a perimeter constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09592 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On some functionals involving torsional rigidity, principal eigenvalue and perimeter Amato, Vincenzo Nitsch, Carlo Trombetti, Cristina Villone, Federico Spectral Theory Analysis of PDEs 49Q10, 35J25, 49K20, 35J05 In this paper we study some relationships between the first Dirichlet eigenvalue $Λ(Ω)$ and the torsional rigidity $T(Ω)$ of a domain $Ω$. We consider the problem of optimizing the product $Λ(Ω)T(Ω)$ among sets with prescribed perimeter, both in the class of open sets with finite perimeter and within the class of convex domains. We also present local results for the quantity $Λ(Ω)T(Ω)^q$, with $q>0$, under either a volume or a perimeter constraint. |
| title | On some functionals involving torsional rigidity, principal eigenvalue and perimeter |
| topic | Spectral Theory Analysis of PDEs 49Q10, 35J25, 49K20, 35J05 |
| url | https://arxiv.org/abs/2601.09592 |