The inclusion of Stekloff eigenvalues by boundary data approximation
type: Item
instance of: scholarly article
title: The inclusion of Stekloff eigenvalues by boundary data approximation
zbMATH Open document ID: 0815.35077
DOI: 10.1007/BF00945928
author: Ralph Ennenbach
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1995-06-27T00:00:00Z
review text: Let \(G\) be a simply connected plane domain bounded by an analytic curve \(\Gamma\). The following Stekloff eigenvalue problem \[ \Delta u = 0 \quad \text{in} \quad G \quad \text{and} \quad {\partial u \over \partial n} = pu \quad \text{ on } \Gamma \] is considered. Eigenvalue inclusion theorems are derived to obtain two sided bounds for the eigenvalues. The test functions \(u_ *\) must satisfy only the equation \(\Delta u_ * = 0\). The applied test functions build up from the singularity functions \(\ln | x - y_ n |\), where the source points \(y_ n\) lie in the exterior of \(G\). The eigenvalue inclusion theorem is combined with the boundary collocation method. Numerical examples illustrate the advantage of the presented method. Some possibilities of the extension are also mentioned. The inclusion theorems can be interpreted as norm inequalities, too.
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 636030
zbMATH Keywords: Steklov eigenvalue problem
zbMATH Keywords: collocation
zbMATH Keywords: inclusion theorem
reviewed by: István Ecsedi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 636030