In this conference, generalizing to the non smooth case already existing results, we prove that, for any convex planar set Ω, the first non-trivial Neumann eigenvalue μ_1(Ω) of the Hermite operator is greater than or equal to 1. Furthermore, and this is our main result, under some additional assumptions on Ω, we show that μ_1(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.
Sharp bounds for Neumann eigenvalues of the Hermite operator / Brandolini, Barbara. - (2015). (Intervento presentato al convegno 4th Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's tenutosi a Gaeta nel 26 maggio 2015).
Sharp bounds for Neumann eigenvalues of the Hermite operator
BRANDOLINI, BARBARA
2015
Abstract
In this conference, generalizing to the non smooth case already existing results, we prove that, for any convex planar set Ω, the first non-trivial Neumann eigenvalue μ_1(Ω) of the Hermite operator is greater than or equal to 1. Furthermore, and this is our main result, under some additional assumptions on Ω, we show that μ_1(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.
