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The equality case in a Poincare-Wirtinger type inequality

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    0466556 - ÚJF 2017 RIV CH eng J - Journal Article
    Brandolini, B. - Chiacchio, F. - Krejčiřík, David - Trombetti, C.
    The equality case in a Poincare-Wirtinger type inequality.
    Accademia Nazionale dei Lincei. Atti. Matematica e Applicazioni. Rendiconti. Roč. 27, č. 4 (2016), s. 443-464. ISSN 1120-6330. E-ISSN 1720-0768
    R&D Projects: GA ČR(CZ) GA14-06818S
    Institutional support: RVO:61389005
    Keywords : Hermite operator * Neumann eigenvalues * thin strips
    Subject RIV: BE - Theoretical Physics
    Impact factor: 1.096, year: 2016

    t is known that, for any convex planar set Omega, the first non-trivial Neumann eigenvalue mu(1)(Omega) of the Hermite operator is greater than or equal to 1. Under the additional assumption that W is contained in a strip, we show that mu(1)(Omega) = 1 if and only if W is any strip. The study of the equality case requires, among other things, an asymptotic analysis of the eigenvalues of the Hermite operator in thin domains.
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