Exercises on the theme of continuous symmetrization

Alexander Solynin

doi:10.1007/s40315-020-00331-y

Exercises on the theme of continuous symmetrization

Alexander Solynin

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Abstract: In this paper, we discuss the P\'{o}lya-Szeg\"{o} continuous symmetrization and its applications to isoperimetric inequalities. In particular, we survey results concerning monotonicity properties of certain characteristics, including torsional rigidity of cylindrical beams and principal frequency of a uniformly stretched elastic membrane of a drum, of triangles and other domains. Several remaining open problems on continuous symmetrization and relevant properties of domains and functions also are discussed.

Original language	English
Pages (from-to)	45 pages
Journal	Computational Methods and Function Theory
DOIs	https://doi.org/10.1007/s40315-020-00331-y
State	Published - Jul 13 2020

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AB - Abstract: In this paper, we discuss the P\'{o}lya-Szeg\"{o} continuoussymmetrization and its applications to isoperimetric inequalities.In particular, we survey results concerning monotonicityproperties of certain characteristics, including torsionalrigidity of cylindrical beams and principal frequency of auniformly stretched elastic membrane of a drum, of triangles andother domains. Several remaining open problems on continuoussymmetrization and relevant properties of domains and functionsalso are discussed.

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