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

We consider the eigenvalue problem with Robin boundary condition Δu + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω, where Ω ⊂ ℝ n , 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 thi...

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Bibliographic Details
Published in:Mathematical modelling and analysis Vol. 22; no. 1; pp. 37 - 51
Main Author: Filinovskiy, Alexey V.
Format: Journal Article
Language:English
Published: Taylor & Francis 02.01.2017
Vilnius Gediminas Technical University
Subjects:
asymptotic behavior
Asymptotic expansions
Boundaries
Boundary value problems
Dirichlet problem
Eigenfunctions
Eigenvalues
eigenvalues and eigenfunctions
Estimates
Laplace operator
large parameter
Mathematical models
Mathematical research
Parameters
Robin boundary condition
Laplace operator
Robin boundary condition
large parameter
asymptotic behavior
eigenvalues and eigenfunctions
ISSN:1392-6292, 1648-3510
Online Access:Get full text
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Summary:We consider the eigenvalue problem with Robin boundary condition Δu + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω, where Ω ⊂ ℝ n , 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.
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ISSN:1392-6292
1648-3510
DOI:10.3846/13926292.2017.1263244