© 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 ...

In this paper we prove some analogs of the St Venant conjecture on the torsional rigidity. One of them is connected with Leavitt and Ungar's inequality.

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 ...

We consider the Saint-Venant functional P for the torsional rigidity in an arbitrary plane or spatial domain. The main result of this paper is the sharp estimate P < (4/n)m, where n is the dimension of the space, and m is ...

Euclidean moments of simply connected plane domains are investigated. The moments are defined as the pth power of the L p-norms of the distance function to the boundary of the domain. As was shown by Avkhadiev (1998) the ...