A note on the ellipticity of the single layer potential in two-dimensional linear elastostatics
type: Item
instance of: scholarly article
title: A note on the ellipticity of the single layer potential in two-dimensional linear elastostatics
zbMATH Open document ID: 1096.35040
author: O. Steinbach
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-10T00:00:00Z
review text: It is well-known that in the case of two-dimensional Laplace operator the corresponding single layer potential of the Laplace operator is \(H^{-1/2}(\Gamma)\)-elliptic, if the domain \(\Omega\) satisfies the scaling condition \(\operatorname{diam} \Omega<1\). In the case of the system of planar linear elastostatics it seems to be an open problem, how to scale the computational domain \(\Omega\) to ensure the \([H^{-1/2}(\Gamma)]^2\)-ellipticity of the single layer potential \(V\). In this note the author applies the ideas of the proof for the single layer potential of the Laplace operator to show the ellipticity of the single layer potential \(V\) if a suitable scaling of the computational domain \(\Omega\) is applied.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 2085904
zbMATH Keywords: planar linear elasticity
zbMATH Keywords: single layer potential
zbMATH Keywords: ellipticity
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.10.053
OpenAlex ID: W2052729565
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DOI: 10.1016/J.JMAA.2003.10.053
description: scientific article; zbMATH DE number 2085904