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

IF 0.4 4区数学 Q4 MATHEMATICS

Contributions To Discrete Mathematics 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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来源期刊

Contributions To Discrete Mathematics MATHEMATICS-

CiteScore

1.30

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0.00%

发文量

期刊介绍： Contributions to Discrete Mathematics (ISSN 1715-0868) is a refereed e-journal dedicated to publishing significant results in a number of areas of pure and applied mathematics. Based at the University of Calgary, Canada, CDM is free for both readers and authors, edited and published online and will be mirrored at the European Mathematical Information Service and the National Library of Canada.