ABOUT A TRANSFORMATION OF SCHWARZ PROBLEM
В. Г. Николаев · Vestnik of Samara University Natural Science Series · 2012
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.