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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 8, Pages 59–68 (Mi ivm7119)  

This article is cited in 4 scientific papers (total in 4 papers)

Isoperimetric monotony of the $L^p$-norm of the warping function of a plane simply connected domain

R. G. Salakhudinov

Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, Kazan, Russia

Abstract: 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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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:8, 48–56

Bibliographic databases:

UDC: 517.5+517.956
Received: 24.09.2008

Citation: R. G. Salakhudinov, “Isoperimetric monotony of the $L^p$-norm of the warping function of a plane simply connected domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 8, 59–68; Russian Math. (Iz. VUZ), 54:8 (2010), 48–56

Citation in format AMSBIB
\Bibitem{Sal10}
\by R.~G.~Salakhudinov
\paper Isoperimetric monotony of the $L^p$-norm of the warping function of a~plane simply connected domain
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 8
\pages 59--68
\mathnet{http://mi.mathnet.ru/ivm7119}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2752579}
\elib{https://elibrary.ru/item.asp?id=14369657}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 8
\pages 48--56
\crossref{https://doi.org/10.3103/S1066369X10080074}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649613727}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. G. Salakhudinov, “Integral Properties of the Classical Warping Function of a Simply Connected Domain”, Math. Notes, 92:3 (2012), 412–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Salakhudinov R.G., “Refined Inequalities for Euclidean Moments of a Domain with Respect to its Boundary”, SIAM J. Math. Anal., 44:4 (2012), 2949–2961  crossref  mathscinet  zmath  isi  elib
    3. R. G. Salakhudinov, “Isoperimetric inequalities for $L^p$-norms of the stress function of a multiply connected plane domain”, Russian Math. (Iz. VUZ), 57:9 (2013), 62–66  mathnet  crossref
    4. Salakhudinov R.G., “Payne Type Inequalities for l-P-Norms of the Warping Functions”, J. Math. Anal. Appl., 410:2 (2014), 659–669  crossref  mathscinet  zmath  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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