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

    Alexey V. Filinovskiy Affiliation

Abstract

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.

Keyword : Laplace operator, Robin boundary condition, eigenvalues and eigenfunctions, large parameter, asymptotic behavior

How to Cite
Filinovskiy, A. V. (2017). On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter. Mathematical Modelling and Analysis, 22(1), 37-51. https://doi.org/10.3846/13926292.2017.1263244
Published in Issue
Jan 11, 2017
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