Where to place a spherical obstacle so as to maximize the second Dirichlet eigenvalue

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dc.creatorSoufi, Ahmad El
dc.creatorKiwan, Rola
dc.date2007-12-12
dc.date.accessioned2026-07-07T10:00:08Z
dc.date.available2026-07-07T10:00:08Z
dc.descriptionWe prove that among all doubly connected domains of $\mathbb{R}^n$ bounded by two spheres of given radii, the second eigenvalue of the Dirichlet Laplacian achieves its maximum when the spheres are concentric (spherical shell). The corresponding result for the first eigenvalue has been established by Hersch in dimension 2, and by Harrell, Kröger and Kurata and Kesavan in any dimension. We also prove that the same result remains valid when the ambient space $\mathbb{R}^n$ is replaced by the standard sphere $\mathbb{S}^n$ or the hyperbolic space $\mathbb{H}^n$ .
dc.descriptionTo appear in Communications in Pure and Applied Analysis
dc.identifierhttps://arxiv.org/abs/0712.2033
dc.identifierhttp://arxiv.org/abs/0712.2033
dc.identifierCommunications on Pures and Applied Analysis 7, 5 (2008) 1193 -- 1201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168249
dc.subjectMetric Geometry
dc.subjectSpectral Theory
dc.subject35P15, 49R50, 58J50
dc.titleWhere to place a spherical obstacle so as to maximize the second Dirichlet eigenvalue
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