Geodesic
A~constructive characterization of harmonic functions in domains with quasiconformal boundaries
Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 441-454

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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. 
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     author = {V. V. Andrievskii},
     title = {A~constructive characterization of harmonic functions in domains with quasiconformal boundaries},
     journal = {Izvestiya. Mathematics },
     pages = {441--454},
     publisher = {mathdoc},
     volume = {34},
     number = {2},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a11/}
}
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V. V. Andrievskii. A~constructive characterization of harmonic functions in domains with quasiconformal boundaries. Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 441-454. http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a11/