Extremal eigenvalue problems for composite membranes. II
type: Item
instance of: scholarly article
title: Extremal eigenvalue problems for composite membranes. II
zbMATH Open document ID: 0709.73045
DOI: 10.1007/BF01447326
author: Steven J. Cox
author: Joyce McLaughlin
published in: Applied Mathematics and Optimization
publication date: 1990-01-01T00:00:00Z
review text: This work is a continuation of a paper with the same title [part I: see the foregoing entry (Zbl 0709.73044)]. The optimality conditions are obtained as an immediate consequence of a minimum principle. A direct approach is taken to characterize the solution of the optimal design problem. This characterization allows to use the linear membrane equation in the form of a nonlinear eigenvalue problem. From this the results are obtained on the geometry of the level sets of eigenfunctions and subsequently on the geometry of the extremizers of \(\rho \to \lambda_ 1(\rho)\).
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 49R50
Mathematics Subject Classification ID: 49J27
zbMATH DE Number: 4167169
zbMATH Keywords: optimality conditions
zbMATH Keywords: optimal design problem
zbMATH Keywords: nonlinear eigenvalue problem
reviewed by: István Ecsedi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01447326
OpenAlex ID: W2078293634
description: scientific article; zbMATH DE number 4167169