ABOUT A TRANSFORMATION OF SCHWARZ PROBLEM



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Abstract

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.

About the authors

V.G. Nikolaev

Novgorod State University

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Email: morenov.sv@ssau.ru

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Copyright (c) 2012 Nikolaev V.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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