On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms
| dc.creator | Anisa, M H C | |
| dc.creator | Aithal, A R | |
| dc.date | 2005-03-05 | |
| dc.date.accessioned | 2026-07-07T05:17:42Z | |
| dc.date.available | 2026-07-07T05:17:42Z | |
| dc.description | Let $B_1$ be a ball of radius $r_1$ in $S^n(\Hy^n)$, and let $B_0$ be a smaller ball of radius $r_0$ such that $\bar{B_0}\subset B_1$. For $S^n$ we consider $r_1< π$. Let $u$ be a solution of the problem $-\La u =1$ in $\Om := B_1\setminus \bar{B_0}$ vanishing on the boundary. It is shown that the associated functional $J(\Om)$ is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian on $\Om$ is maximal if and only if the balls are concentric. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503097 | |
| dc.identifier | http://arxiv.org/abs/math/0503097 | |
| dc.identifier | Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 1, February 2005, pp. 93-102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74402 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.subject | 35J25; 35P15; 53C21; 58J32; 58J50 | |
| dc.title | On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms | |
| dc.type | text |