Abstract
In this paper, we study the analogue in Gauss space of Lord Rayleigh’s conjecture for the clamped plate. We show that the first eigenvalue of the bi-Hermite operator in a bounded domain is bounded below by a constant CV times the corresponding eigenvalue of a half-space with the same Gaussian measure V. Similar results are established on unbounded domains. We use rearrangement methods similar to Talenti’s for the Euclidean clamped plate. We obtain our constant CV following the Euclidean approach of Ashbaugh and Benguria, and we find a numerical bound CV≥ 0.91 by solving an associated minimization problem in terms of parabolic cylinder functions.
Original language | English (US) |
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Pages (from-to) | 1977-2005 |
Number of pages | 29 |
Journal | Annali di Matematica Pura ed Applicata |
Volume | 195 |
Issue number | 6 |
DOIs | |
State | Published - Dec 1 2016 |
Keywords
- Clamped plate
- Comparison results
- Gauss space
- Parabolic cylinder functions
- Symmetrization