The clamped plate in Gauss space

L. M. Chasman, Jeffrey J. Langford

    Research output: Contribution to journalArticlepeer-review

    2 Scopus citations


    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
    Issue number6
    StatePublished - Dec 1 2016


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

    Fingerprint Dive into the research topics of 'The clamped plate in Gauss space'. Together they form a unique fingerprint.

    Cite this