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

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 isoperimetricallymonotone with respect to the free parameter. A particular case of the proved result is the Payne inequality for the torsional rigidity of G. © 2013 Allerton Press, Inc.