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• W2900792066 abstract "We consider the analogue of Rayleigh's conjecture for the clamped plate in Euclidean space weighted by a log-convex density. We show that the lowest eigenvalue of the bi-Laplace operator with drift in a given domain is bounded below by a constant $C(V,n)$ times the lowest eigenvalue of a centered ball of the same volume; the constant depends on the volume $V$ of the domain and the dimension $n$ of the ambient space. Our result is driven by a comparison theorem in the spirit of Talenti, and the constant $C(V,n)$ is defined in terms of a minimization problem following the work of Ashbaugh and Benguria. When the density is an anti-Gaussian, we estimate $C(V,n)$ using a delicate analysis that involves confluent hypergeometric functions, and we illustrate numerically that $C(V,n)$ is close to $1$ for low dimensions." @default.
• W2900792066 created "2018-11-29" @default.
• W2900792066 creator A5010401077 @default.
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• W2900792066 date "2018-11-15" @default.
• W2900792066 modified "2023-09-27" @default.
• W2900792066 title "On Clamped Plates with Log-Convex Density" @default.
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• W2900792066 hasPublicationYear "2018" @default.
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