A method of symmetrizing functions and its application to certain problems in elasticity theory for non-uniform bodies
type: Item
instance of: scholarly article
title: A method of symmetrizing functions and its application to certain problems in elasticity theory for non-uniform bodies
zbMATH Open document ID: 0724.73046
DOI: 10.1016/0021-8928(88)90093-7
author: S. R. Brudnyĭ
author: Efim I. Shifrin
published in: Journal of Applied Mathematics and Mechanics
publication date: 1988-01-01T00:00:00Z
review text: A symmetrization operation is introduced for functions defined in bounded domains and vanishing on the boundary. The properties of the operation introduced are studied and its connection with Schwarz symmetrization is analyzed. Examples are considered of the application of the apparatus developed for constructing isoperimetric estimates in problems of torsion and longitudinal vibrations of an inhomogeneous rod. The stiffness estimate obtained in the problem of the torsion of a nonuniform rod is a generalization of the Polya isoperimetric inequality known in the theory of elasticity for the stiffness of a uniform rod under torsion.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 49Q20
zbMATH DE Number: 4195309
zbMATH Keywords: symmetrization operation
zbMATH Keywords: Schwarz symmetrization
zbMATH Keywords: isoperimetric estimates
zbMATH Keywords: torsion
zbMATH Keywords: longitudinal vibrations
zbMATH Keywords: inhomogeneous rod
zbMATH Keywords: stiffness estimate
MaRDI profile type: Publication
full work available at URL: 0021-8928(88)90093-7
OpenAlex ID: W2057825768
cites work: Q3284383
cites work: On The Zeros Of Solutions Of Second-Order Linear Differential Equations
cites work: Q5779489
description: scientific article; zbMATH DE number 4195309