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Mat. Zametki, 2006, Volume 80, Issue 4, Pages 601–612 (Mi mz2853)  

This article is cited in 1 scientific paper (total in 1 paper)

Estimation of the $L_p$-norms of stress functions for finitely connected plane domains

R. G. Salakhudinov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: Let $u(x,G)$ be the classical stress function of a finitely connected plane domain $G$. The isoperimetric properties of the $L^p$-norms of $u(x,G)$ are studied. Payne's inequality for simply connected domains is generalized to finitely connected domains. It is proved that the $L^p$-norms of the functions $u(x,G)$ and $u^{-1}(x,G)$ strictly decrease with respect to the parameter $p$, and a sharp bound for the rate of decrease of the $L^p$-norms of these functions in terms of the corresponding $L^p$-norms of the stress function for an annulus is obtained. A new integral inequality for the $L^p$-norms of $u(x,G)$, which is an analog of the inequality obtained by F. G. Avkhadiev and the author for the $L^p$-norm of conformal radii, is proved.

DOI: https://doi.org/10.4213/mzm2853

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English version:
Mathematical Notes, 2006, 80:4, 567–577

Bibliographic databases:

UDC: 517.5+517.956.225
Received: 04.09.2003

Citation: R. G. Salakhudinov, “Estimation of the $L_p$-norms of stress functions for finitely connected plane domains”, Mat. Zametki, 80:4 (2006), 601–612; Math. Notes, 80:4 (2006), 567–577

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Hasnaoui A., Hermi L., “Isoperimetric Inequalities for a Wedge-Like Membrane”, Ann. Henri Poincare, 15:2 (2014), 369–406  crossref  mathscinet  zmath  adsnasa  isi  scopus
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