Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2019
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914965935357952 |
|---|---|
| author | Paoli, Gloria Piscitelli, Gianpaolo Trani, Leonardo |
| author_facet | Paoli, Gloria Piscitelli, Gianpaolo Trani, Leonardo |
| contents | We study, in dimension $n\geq2$, the eigenvalue problem and the torsional rigidity for the $p$-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_00362 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes Paoli, Gloria Piscitelli, Gianpaolo Trani, Leonardo Analysis of PDEs 35J25, 35J92, 35P15, 47J30 We study, in dimension $n\geq2$, the eigenvalue problem and the torsional rigidity for the $p$-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed. |
| title | Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes |
| topic | Analysis of PDEs 35J25, 35J92, 35P15, 47J30 |
| url | https://arxiv.org/abs/1908.00362 |