带漂移的狄利克雷-拉普拉斯算子的前两个特征值之比的估计

Pub Date : 2021-01-01 DOI:10.47443/cm.2021.0043

Şerban Bărbuleanu, M. Mihăilescu, Denisa Stancu-Dumitru

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引用次数: 0

摘要

设Ω∧R是一个开有界集合。考虑在齐次Dirichlet边界条件(∂Ω上u = 0)下，漂移项为−∆u−x·∇u = λu的拉普拉斯算子的特征值问题。用λ1(Ω)和λ2(Ω)表示问题的前两个特征值。我们发现λ2(Ω)λ1(Ω)≤1 + 4N−1。特别地，我们补充了Thompson [Stud]得到的类似结果。达成。数学。48(1969)281-283]对于拉普拉斯算子的经典特征值问题。

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Estimates for the ratio of the first two eigenvalues of the Dirichlet-Laplace operator with a drift

Abstract Let Ω ⊂ R be an open and bounded set. Consider the eigenvalue problem of the Laplace operator with a drift term −∆u−x ·∇u = λu in Ω subject to the homogeneous Dirichlet boundary condition (u = 0 on ∂Ω). Denote by λ1(Ω) and λ2(Ω) the first two eigenvalues of the problem. We show that λ2(Ω)λ1(Ω) ≤ 1 + 4N−1. In particular, we complement a similar result obtained by Thompson [Stud. Appl. Math. 48 (1969) 281–283] for the classical eigenvalue problem of the Laplace operator.

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