Department of High Mathematics, Faculty of Fundamental Sciences, Bauman Moscow State Technical University, 2nd Baumanskaya st. 5, 105005 Moscow, Russia; Department of Differential Equations, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory 1, 119991 Moscow, Russia
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.
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
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