Asymptotics for the spectrum of the Dirichlet Laplacian on horn-shaped regions (Q2758104)
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scientific article; zbMATH DE number 1679400
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotics for the spectrum of the Dirichlet Laplacian on horn-shaped regions |
scientific article; zbMATH DE number 1679400 |
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2001
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spectral asymptotics
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Dirichlet Laplace operator
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0.9514976
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0.94075346
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0.92736536
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0.9259398
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0.91819286
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0.9179622
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0.9140935
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0.9129256
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Asymptotics for the spectrum of the Dirichlet Laplacian on horn-shaped regions (English)
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The authors prove asymptotic estimates of spectra of the Dirichlet Laplace operators on horn-shaped domains in \(\mathbb{R}^m\) that are derived from star-shaped domains in \(\mathbb{R}^{m-1}\) by means of the generating function \((1+x)^{-\alpha}\). These are extensions of results of \textit{G. V. Rozenblyum} [Mat. Sb., Nov. Ser. 89(131), 234--247 (1972; Zbl 0267.35063), Probl. Mat. Analiz. 4, 95--106 (1973; Zbl 0247.45003)]. For a wide range of the parameter \(\alpha\) the authors obtain two-term asymptotics and a remainder estimate for the Dirichlet counting function.
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