THE SYMMETRIZATION METHOD IN PROBLEMS ON NONOVERLAPPING DOMAINS

Abstract

A new approach to the use of symmetrization is considered. Sterner symmetrization is taken as the main tool. An arbitrary symmetrization transformation connected with a given quadratic differential is obtained by successive application of the mapping and Steiner symmetrization. As a consequence of the main theorem, the corresponding results of Lavrent'ev, Goluzin, Jenkins, and others are refined and generalized to the case of domains of arbitrary connectivity (not necessarily having a filling).Bibliography: 21 titles.