Isoperimetric inequality for torsional rigidity in multidimensional domains
Farit Gabidinovich Avkhadiev · Russian Mathematics · 2012
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 the harmonic mean of moments of inertia of the domain about the coordinate planes. The extremal domains are ellipsoids of a special kind. Thus, we obtain a generalization of the isoperimetric inequality proved by E. Nicolay for the torsional rigidity of simply connected plane domains.