Exercises on the theme of continuous symmetrization

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Abstract: In this paper, we discuss the P\'{o}lya-Szeg\"{o} continuous<br>symmetrization and its applications to isoperimetric inequalities.<br>In particular, we survey results concerning monotonicity<br>properties of certain characteristics, including torsional<br>rigidity of cylindrical beams and principal frequency of a<br>uniformly stretched elastic membrane of a drum, of triangles and<br>other domains. Several remaining open problems on continuous<br>symmetrization and relevant properties of domains and functions<br>also are discussed.
Original languageEnglish
Pages (from-to)45 pages
JournalComputational Methods and Function Theory
StatePublished - Jul 13 2020


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