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• W2023510134 abstract "We consider the Dirichlet Laplacian Δ∈ in a family of bounded domains {−a < x < b, 0 < y < eh(x)}. The main assumption is that x = 0 is the only point of global maximum of the positive, continuous function h(x). We find the two-term asymptotics in e → 0 of the eigenvalues and the one-term asymptotics of the corresponding eigenfunctions. The asymptotic formulas obtained involve the eigenvalues and eigenfunctions of an auxiliary ODE on ℝ that depends on the behavior of h(x) as x → 0. The proof is based on a detailed study of the resolvent of the operator Δ∈." @default.
• W2023510134 created "2016-06-24" @default.
• W2023510134 creator A5022267593 @default.
• W2023510134 creator A5060740466 @default.
• W2023510134 date "2009-03-01" @default.
• W2023510134 modified "2023-10-02" @default.
• W2023510134 title "On the spectrum of the Dirichlet Laplacian in a narrow strip" @default.
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• W2023510134 doi "https://doi.org/10.1007/s11856-009-0032-y" @default.
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