On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

dc.creatorAnisa, M H C
dc.creatorAithal, A R
dc.date2005-03-05
dc.date.accessioned2026-07-07T05:17:42Z
dc.date.available2026-07-07T05:17:42Z
dc.descriptionLet $B_1$ 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.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0503097
dc.identifierhttp://arxiv.org/abs/math/0503097
dc.identifierProc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 1, February 2005, pp. 93-102
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74402
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject35J25; 35P15; 53C21; 58J32; 58J50
dc.titleOn two functionals connected to the Laplacian in a class of doubly connected domains in space-forms
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