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

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Abstract

Let u(x,G) be the stress function of a multiply connected plane domain G. We construct new domain functionals depending on this stress function which are isoperimetrically monotone with respect to the free parameter. A particular case of the proved result is the Payne inequality for the torsional rigidity of G.

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References

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    R. G. Salakhudinov

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  1. R. G. Salakhudinov
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Correspondence to R. G. Salakhudinov.

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Original Russian Text © R.G. Salakhudinov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 9, pp. 75–80.

Submitted by F.G. Avkhadiev

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Salakhudinov, R.G. Isoperimetric inequalities for L p-norms of the stress function of a multiply connected plane domain. Russ Math. 57, 62–66 (2013). https://doi.org/10.3103/S1066369X13090107

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  • DOI: https://doi.org/10.3103/S1066369X13090107

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