On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter

Mathematical Modelling and Analysis

Alexey V. Filinovskiy¹ 

[1] Department of High Mathematics, Faculty of Fundamental Sciences, Bauman Moscow State Technical University, 2nd Baumanskaya st. 5, 105005 Moscow, Russia;

关键词: Laplace operator;    Robin boundary condition;    eigenvalues and eigenfunctions;    large parameter;    asymptotic behavior;   

DOI  :  10.3846/13926292.2017.1263244

来源: DOAJ

【 摘 要 】

We consider the eigenvalue problem with Robin boundary condition ∆u + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω, where Ω ⊂ Rn , n ≥ 2 is a bounded domain with a smooth boundary, ν is the outward unit normal, α is a real parameter. We obtain two terms of the asymptotic expansion of simple eigenvalues of this problem for α → +∞. We also prove an estimate to the difference between Robin and Dirichlet eigenfunctions.

【 授权许可】

Unknown