On compact classes of solutions of Dirichlet problem in simply connected domains

Abstract

The article is devoted to questions concerning the problems of compactness of solutions of the Dirichlet problem for the Beltrami equation in some simply connected domain. In terms of prime ends, we have proved results of a detailed form for the case when the maximal dilations of these solutions satisfy certain integral constraints. In addition, in this article we have proved theorems on the local and global behavior of plane and spatial mappings with direct and inverse modulus conditions.