A~constructive characterization of harmonic functions in domains with quasiconformal boundaries

V. V. Andrievskii

Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 441-454.

Résumé

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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