Geodesic
Continuous and bounded harmonic functions. Exact and approximate methods
Numerical methods and programming, Tome 8 (2007) no. 1, pp. 38-60

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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.
Keywords: harmonic functions, double-layer potential, unstable problems, regularization methods, ill-posed problems. 
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     author = {V. A. Morozov and \`E. M. Muhamadiev and A. B. Nazimov},
     title = {Continuous and bounded harmonic functions. {Exact} and approximate methods},
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     pages = {38--60},
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     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2007_8_1_a6/}
}
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V. A. Morozov; È. M. Muhamadiev; A. B. Nazimov. Continuous and bounded harmonic functions. Exact and approximate methods. Numerical methods and programming, Tome 8 (2007) no. 1, pp. 38-60. http://geodesic.mathdoc.fr/item/VMP_2007_8_1_a6/