The clamped plate in Gauss space

L. M. Chasman, Jeffrey J. Langford

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    2 Scopus citations

    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 languageEnglish (US)
    Pages (from-to)1977-2005
    Number of pages29
    JournalAnnali di Matematica Pura ed Applicata
    Volume195
    Issue number6
    DOIs
    StatePublished - Dec 1 2016

    Keywords

    • Clamped plate
    • Comparison results
    • Gauss space
    • Parabolic cylinder functions
    • Symmetrization

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