Some shape functionals for the $k$-Hessian equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912605253140480 |
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| author | Masiello, Alba Lia Salerno, Francesco |
| author_facet | Masiello, Alba Lia Salerno, Francesco |
| contents | For a non-empty, bounded, open, and convex set of class $C^2$, we consider the Torsional Rigidity associated to the $k$-Hessian operator. We first prove Pólya type lower bound for the $k$-Torsional Rigidity in any dimension; then, in order to investigate optimal sets in the Pólya type inequality, we provide two quantitative estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some shape functionals for the $k$-Hessian equation Masiello, Alba Lia Salerno, Francesco Analysis of PDEs 35J96, 52A39, 35J60 For a non-empty, bounded, open, and convex set of class $C^2$, we consider the Torsional Rigidity associated to the $k$-Hessian operator. We first prove Pólya type lower bound for the $k$-Torsional Rigidity in any dimension; then, in order to investigate optimal sets in the Pólya type inequality, we provide two quantitative estimates. |
| title | Some shape functionals for the $k$-Hessian equation |
| topic | Analysis of PDEs 35J96, 52A39, 35J60 |
| url | https://arxiv.org/abs/2509.21313 |