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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 260, Pages 75–96
(Mi tm587)
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This article is cited in 6 scientific papers (total in 6 papers)
Spectral Stability of the Robin Laplacian
V. I. Burenkov, M. Lanza de Cristoforisa a Department of Pure and Applied Mathematics, University of Padua
Abstract:
We consider the Robin Laplacian in two bounded regions $\Omega_1$ and $\Omega_2$ of $\mathbb R^N$ with Lipschitz boundaries and such that $\Omega_2\subset\Omega_1$, and we obtain two-sided estimates for the eigenvalues $\lambda_{n,2}$ of the Robin Laplacian in $\Omega_2$ via the eigenvalues $\lambda_{n,1}$ of the Robin Laplacian in $\Omega_1$. Our estimates depend on the measure of the set difference $\Omega_1\!\setminus\Omega_2$ and on suitably defined characteristics of vicinity of the boundaries $\partial\Omega_1$ and $\partial\Omega_2$, and of the functions defined on $\partial\Omega_1$ and on $\partial\Omega_2$ that enter the Robin boundary conditions.
Received in May 2007
Citation:
V. I. Burenkov, M. Lanza de Cristoforis, “Spectral Stability of the Robin Laplacian”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 75–96; Proc. Steklov Inst. Math., 260 (2008), 68–89
Linking options:
https://www.mathnet.ru/eng/tm587 https://www.mathnet.ru/eng/tm/v260/p75
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