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

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.
Settore MAT/05 - Analisi Matematica
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/493978
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