© 2018, Pleiades Publishing, Ltd. Denote by P(G) the torsional rigidity of a simply connected plane domain G, and by I2(G) the Euclidean moment of inertia of G. In 1995 F.G. Avkhadiev proved that P(G) and I2(G) are comparable ...

Let u(z,G) be the classical warping function of a simply connected domain G. We prove that the L p-norms of the warping function with different exponents are related by a sharp isoperimetric inequality, including the ...

Let G be a simply connected domain and let u(x,G) be its warping function. We prove that L p -norms of functions u and u -1 are monotone with respect to the parameter p. This monotony also gives isoperimetric inequalities ...

Let u(x, G) be a warping function of a multiply connected plane domain G. A new physical functional of u(x, G) with an isoperimetric monotonicity property is constructed. It is proved that Lp- and Lq-norms of the warping ...