Reverse Faber-Krahn inequality for the $p$-Laplacian in Hyperbolic space
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912063264129024 |
|---|---|
| author | Ghosh, Mrityunjoy Verma, Sheela |
| author_facet | Ghosh, Mrityunjoy Verma, Sheela |
| contents | In this paper, we study the shape optimization problem for the first eigenvalue of the $p$-Laplace operator with the mixed Neumann-Dirichlet boundary conditions on multiply-connected domains in hyperbolic space. Precisely, we establish that among all multiply-connected domains of a given volume and prescribed $(n-1)$-th quermassintegral of the convex Dirichlet boundary (inner boundary), the concentric annular region produces the largest first eigenvalue. We also derive Nagy's type inequality for outer parallel sets of a convex domain in the hyperbolic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_13372 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Reverse Faber-Krahn inequality for the $p$-Laplacian in Hyperbolic space Ghosh, Mrityunjoy Verma, Sheela Analysis of PDEs Differential Geometry Optimization and Control 58C40, 35P15, 35P30, 49R05 In this paper, we study the shape optimization problem for the first eigenvalue of the $p$-Laplace operator with the mixed Neumann-Dirichlet boundary conditions on multiply-connected domains in hyperbolic space. Precisely, we establish that among all multiply-connected domains of a given volume and prescribed $(n-1)$-th quermassintegral of the convex Dirichlet boundary (inner boundary), the concentric annular region produces the largest first eigenvalue. We also derive Nagy's type inequality for outer parallel sets of a convex domain in the hyperbolic space. |
| title | Reverse Faber-Krahn inequality for the $p$-Laplacian in Hyperbolic space |
| topic | Analysis of PDEs Differential Geometry Optimization and Control 58C40, 35P15, 35P30, 49R05 |
| url | https://arxiv.org/abs/2205.13372 |