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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 9, Pages 75–80 (Mi ivm8831)  
This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

Isoperimetric inequalities for $L^p$-norms of the stress function of a multiply connected plane domain

R. G. Salakhudinov

Chair of Mathematical Analysis, Kazan (Volga Region) Federal University, 18 Universitetskaya str., Kazan, 420008 Russia
Full-text PDF (175 kB) Citations (3)
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Abstract: Let $u(x,G)$ be the stress function of a multiply connected plane domain $G$. We construct new functionals depending on the stress function. The constructed functionals are isoperimetrically monotone with respect to the free parameter. A particular case of the proved result is the inequality of obtained by Payne for the torsional rigidity of $G$.
Keywords: stress function, torsional rigidity, Payne inequality, isoperimetric inequalities, isoperimetric monotonicity, symmetrization.
Presented by the member of Editorial Board: F. G. Avkhadiev
Received: 20.03.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 9, Pages 62–66
DOI: https://doi.org/10.3103/S1066369X13090107
Bibliographic databases:
Document Type: Article
UDC: 517.5+517.956
Language: Russian
Citation: R. G. Salakhudinov, “Isoperimetric inequalities for $L^p$-norms of the stress function of a multiply connected plane domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 9, 75–80; Russian Math. (Iz. VUZ), 57:9 (2013), 62–66
Citation in format AMSBIB
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\by R.~G.~Salakhudinov
\paper Isoperimetric inequalities for $L^p$-norms of the stress function of a~multiply connected plane domain
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 9
\pages 75--80
\mathnet{http://mi.mathnet.ru/ivm8831}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 9
\pages 62--66
\crossref{https://doi.org/10.3103/S1066369X13090107}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84885321406}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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