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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Vydáno v:	Mathematical modelling and analysis Ročník 22; číslo 1; s. 37 - 51
Hlavní autor:	Filinovskiy, Alexey V.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Taylor & Francis 02.01.2017 Vilnius Gediminas Technical University
Témata:	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
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	1392-6292 1648-3510
DOI:	10.3846/13926292.2017.1263244