A sharp lower bound for some Neumann eigenvalues of the Hermite operator

2012/09/27 by Barbara Brandolini, Brandolini, B., Francesco Chiacchio +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1209.6275

openalex publication_date 2012/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the Neumann eigenvalue problem for the Hermite operator defined in a convex, possibly unbounded, planar domain Ω, having one axis of symmetry passing through the origin. We prove a sharp lower bound for the first eigenvalue μ₁^odd(Ω) with an associated eigenfunction odd with respect to the axis of symmetry. Such an estimate involves the first eigenvalue of the corresponding one-dimensional problem. As an immediate consequence, in the class of domains for which μ₁(Ω)=μ₁^odd(Ω), we get an explicit lower bound for the difference between μ(Ω) and the first Neumann eigenvalue of any strip.

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