Geodesic
Isoperimetric inequalities for $L^p$-norms of the stress function of a~multiply connected plane domain
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2013), pp. 75-80

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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. 
@article{IVM_2013_9_a9,
     author = {R. G. Salakhudinov},
     title = {Isoperimetric inequalities for $L^p$-norms of the stress function of a~multiply connected plane domain},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {75--80},
     publisher = {mathdoc},
     number = {9},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_9_a9/}
}
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R. G. Salakhudinov. Isoperimetric inequalities for $L^p$-norms of the stress function of a~multiply connected plane domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2013), pp. 75-80. http://geodesic.mathdoc.fr/item/IVM_2013_9_a9/