Eigenvalues of the Neumann problem in a domain with a thin channel
type: Item
instance of: scholarly article
title: Eigenvalues of the Neumann problem in a domain with a thin channel
zbMATH Open document ID: 1146.35336
published in: Doklady Mathematics
publication date: 2007-01-12T00:00:00Z
review text: The author constructs asymptotics of eigenvalues of the Neumann problem for the Laplace operator \[ \begin{aligned} -\Delta\Psi^{\varepsilon} &= \lambda^{\varepsilon}\Psi^{\epsilon}\quad \text{ at} \quad x \in \Omega_{\varepsilon} \\ \frac{\partial\Psi^{\varepsilon}}{\partial\nu}&= 0 \quad \text{at}\quad x \in \partial\Omega_{\varepsilon}\end{aligned} \] in a three-dimensional domain of dumb bell type with a thin channel \[ \Omega_{\epsilon} = \Omega^{in} \cup \Omega^{ex} \cup \kappa_{\epsilon}, \] where \( 0 < \varepsilon \ll 1\), and \(\nu\) is an outward normal.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 5115903
zbMATH Keywords: Laplace operator
zbMATH Keywords: Neumann problem
zbMATH Keywords: eigenvalues
zbMATH Keywords: asymptotics
zbMATH Keywords: Kronecker symbol
author: R. R. Gadyl'shin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5115903