The equality case in a Poincaré-Wirtinger type inequality

Barbara Brandolini; Barbara Brandolini; Francesco Chiacchio; Cristina Trombetti; David Krejčiřík

The equality case in a Poincaré-Wirtinger type inequality

Barbara Brandolini, Barbara Brandolini, Francesco Chiacchio, Cristina Trombetti, David Krejčiřík

Matematica e Informatica

Risultato della ricerca: Article › peer review

3 Citazioni (Scopus)

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.

Lingua originale	English
pagine (da-a)	443-464
Numero di pagine	22
Rivista	ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI
Volume	27
Stato di pubblicazione	Published - 2016

All Science Journal Classification (ASJC) codes

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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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AU - Trombetti, Cristina

AU - Krejčiřík, David

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N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/493978

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SN - 1120-6330

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JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

ER -

The equality case in a Poincaré-Wirtinger type inequality

Abstract

All Science Journal Classification (ASJC) codes

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