On the Spectrum of the Dirichlet Laplacian in a Narrow Strip
نویسنده
چکیده
We consider the Dirichlet Laplacian ∆ in a family of bounded domains {−a < x < b, 0 < y < h(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 → 0 of the eigenvalues and the one-term asymptotics of the corresponding eigenfunctions. The asymptotic formulae 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 ∆ .
منابع مشابه
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تاریخ انتشار 2007