Interval analysis techniques for boundary value problems of elasticity in two dimensions
type: Item
instance of: scholarly article
title: Interval analysis techniques for boundary value problems of elasticity in two dimensions
zbMATH Open document ID: 1117.65163
author: Irina Mitrea
author: W. Tucker
published in: Journal of Differential Equations
publication date: 2007-02-12T00:00:00Z
review text: From the authors' abstract: It is proved that the \(L^2\) spectral radius of the traction double layer potential operator associated with the Lamé system on an infinite sector in \(\mathbb{R}^2\) is within \(10^{-2}\) from a certain conjectured value which depends explicitly on the aperture of the sector and the Lamé moduli of the system. This type of result is relevant to the spectral radius conjecture as described, e.g., as Problem 3.2.12 in the work by \textit{C. E. Kenig} [Harmonic analysis techniques for second order elliptic boundary value problems, CBMS Reg. Conf. Ser. Math. 83, Am. Math. Soc., Providence, RI (1994)]. The techniques employed in the paper are a blend of classical tools such as Mellin transforms, and Calderón-Zygmund theory, as well as interval analysis-resulting in a computer-aided proof.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 65G40
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 5124482
zbMATH Keywords: Lamé system
zbMATH Keywords: layer potentials
zbMATH Keywords: traction conormal derivative
zbMATH Keywords: spectral radius
zbMATH Keywords: interval analysis
zbMATH Keywords: computer-aided proof
reviewed by: Günter Mayer
describes a project that uses: RODES
describes a project that uses: C-XSC
MaRDI profile type: Publication
full work available at URL: j.jde.2006.10.010
OpenAlex ID: W2071636906
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DOI: 10.1016/J.JDE.2006.10.010
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description: scientific article; zbMATH DE number 5124482