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

• 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; 1648-3510
• DOI: 10.3846/13926292.2017.1263244

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.