Geodesic
Isoperimetric monotony of the $L^p$-norm of the warping function of a plane simply connected domain
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 59-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be a simply connected domain and let $u(x,G)$ be its warping function. We prove that $L^p$-norms of functions $u$ and $u^{-1}$ are monotone with respect to the parameter $p$. This monotony also gives isoperimetric inequalities for norms that correspond to different values of the parameter $p$. The main result of this paper is a generalization of classical isoperimetric inequalities of St. Venant–Pólya and the Payne inequalities.
Keywords: torsional rigidity, isoperimetric inequalities, isoperimetric monotony, Schwarz symmetrization, Kohler-Jobin symmetrization. 
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R. G. Salakhudinov. Isoperimetric monotony of the $L^p$-norm of the warping function of a plane simply connected domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 59-68. http://geodesic.mathdoc.fr/item/IVM_2010_8_a6/

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