On conformal spectral gap estimates of the Dirichlet-Laplacian V. Gol'dshtein, V. A. Pchelintsev, A. Ukhlov
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ArticleContent type: Текст Media type: электронный Subject(s): эллиптические уравнения | Соболева пространства | конформные отображенияGenre/Form: статьи в журналах Online resources: Click here to access online
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St. Petersburg Mathematical Journal Vol. 31, № 2. P. 325-335Abstract: We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains . With the help of these estimates, we obtain asymptotically sharp inequalities of ratios of eigenvalues in the framework of the Payne-Pólya-Weinberger inequalities. These estimates are equivalent to spectral gap estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains in terms of conformal (hyperbolic) geometry.
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We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains . With the help of these estimates, we obtain asymptotically sharp inequalities of ratios of eigenvalues in the framework of the Payne-Pólya-Weinberger inequalities. These estimates are equivalent to spectral gap estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains in terms of conformal (hyperbolic) geometry.
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