A constructive characterization of harmonic functions in domains with quasiconformal boundaries

For the case of a bounded Jordan domain $G\subset\mathbf C$ with quasiconformal boundary, the author solves the problem, posed by V. K. Dzyadyk in the mid-sixties, of a constructive description of the classes of functions that are harmonic in $G$ and continuous on $\overline G$, with given majorant of their modulus of continuity.
Some assertions reflecting the close connection between the geometric structure of $G$ and contour-solid properties of harmonic functions in $G$ are proved.
Bibliography: 23 titles.