Geodesic
About a transformation of Schwarz problem
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2012), pp. 27-34

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We consider the Schwarz problem for vector-valued functions analytic according to Douglis. We prove that under certain conditions on the matrix this problem is reduced to the Dirichlet problem for some equivalent system of second-order PDEs. The reversebility of transformations is proved, and on that ground the theorem of uniqueness is established. A special case when reduction is impossible is also viewed. The examples are given.
Keywords: analytic functions according to Douglis, Schwarz problem, equivalent reduction, uniqueness. 
@article{VSGU_2012_6_a3,
     author = {V. G. Nikolaev},
     title = {About a transformation of {Schwarz} problem},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {27--34},
     publisher = {mathdoc},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2012_6_a3/}
}
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V. G. Nikolaev. About a transformation of Schwarz problem. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2012), pp. 27-34. http://geodesic.mathdoc.fr/item/VSGU_2012_6_a3/