It is known that, for any convex planar set Ω, 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 μ1(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.
The equality case in a Poincaré-Wirtinger type inequality / Brandolini, Barbara; Chiacchio, Francesco; D., Krejcirik; Trombetti, Cristina. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1720-0768. - 27:4(2016), pp. 443-464. [10.4171/RLM/743]
The equality case in a Poincaré-Wirtinger type inequality
BRANDOLINI, BARBARA;CHIACCHIO, FRANCESCO;TROMBETTI, CRISTINA
2016
Abstract
It is known that, for any convex planar set Ω, 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 μ1(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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
