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

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 $G$.