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• W2045649322 endingPage "1201" @default.
• W2045649322 startingPage "1193" @default.
• W2045649322 abstract "We 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 [12] in dimension 2, and by Harrell, Kröger and Kurata [10] and Kesavan [13] in any dimension.<br> 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 $mathbb H^n$." @default.
• W2045649322 created "2016-06-24" @default.
• W2045649322 creator A5033841250 @default.
• W2045649322 creator A5035987627 @default.
• W2045649322 date "2008-01-01" @default.
• W2045649322 modified "2023-10-16" @default.
• W2045649322 title "Where to place a spherical obstacle so as to maximize the second Dirichlet eigenvalue" @default.
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• W2045649322 doi "https://doi.org/10.3934/cpaa.2008.7.1193" @default.
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