On compactness of one class of solutions of the Dirichlet problem

Abstract

We consider the Dirichlet problem for the Beltrami equation in some simply connected domain. We consider the class of all homeomorphic solutions of such a problem with a normalization condition and set-theoretic constraints on their complex characteristics. We have proved the compactness of this class in terms of prime ends for an arbitrary continuous function in the Dirichlet condition.

arXiv admin note: substantial text overlap with arXiv:2105.09373