A method of symmetrizing functions and its application to certain problems in elasticity theory for non-uniform bodies
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.
scientific article; zbMATH DE number 4195309