It is known that, for any convex planar set W, the first non-trivial Neumann eigenvalue μ1 (Ω) of the Hermite operator is greater than or equal to 1. Under the additional assumption that Ω is contained in a strip, we show that β1 (Ω) = 1 if and only if Ω 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.
Brandolini B., Chiacchio F., Krejcirik D., Trombetti C. (2016). The equality case in a Poincaré-Wirtinger type inequality. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 27(4), 443-464 [10.4171/RLM/743].
The equality case in a Poincaré-Wirtinger type inequality
Brandolini B.
;
2016-01-01
Abstract
It is known that, for any convex planar set W, the first non-trivial Neumann eigenvalue μ1 (Ω) of the Hermite operator is greater than or equal to 1. Under the additional assumption that Ω is contained in a strip, we show that β1 (Ω) = 1 if and only if Ω 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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