Continuous and bounded harmonic functions. Exact and approximate methods - Morozov, V.A.; Mukhamadiev, E.M.; Nazimov, A.B. (Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie), 2007)
The problem of representation of functions harmonic on an open square is considered for the case when these functions satisfy one of the following conditions: a) they have continuous extensions to the closed square and b) they are bounded in the open square. A full description of these classes of harmonic functions is obtained in terms of the properties of boundary values, double-layer potential densities, and the intrinsic properties of harmonic functions in an open square.