On compactness of classes of solutions of the Dirichlet problem with restrictions of the theoretics-set type

TL;DR

This paper proves theorems on the compactness of classes of solutions to the Dirichlet problem involving Beltrami equations with specific constraints, advancing understanding of solution behavior in complex analysis.

Contribution

It introduces new compactness results for classes of solutions to the Dirichlet problem with Beltrami equations under set-theoretic restrictions, extending prior theoretical frameworks.

Findings

Established compactness theorems for solution classes

Derived results for solutions in Jordan domains

Connected solution properties to theoretical-set constraints

Abstract

We have proved theorems on compact classes of homeomorphisms with hydrodynamic normalization that are solutions of the Beltrami equation, whose characteristics are compactly supported and satisfy certain constraints of the theoretical-set type. As a consequence, we obtained results on compact classes of solutions of corresponding Dirichlet problems considered in some Jordan domain.