On Solutions to the Schwarz Problem in a Disk in the Three-Dimensional Case

We consider the Schwarz problem for first order elliptic systems in the plane. We obtain the conditions on three– and two-dimensional matrices J admitting nondiagonal Jordan form under which a solution to the Schwarz problem in an arbitrary disk exists and is unique in Hölder classes. We describe an algorithm for constructing the solution. Bibliography: 5 titles.

This is a preview of subscription content, log in to check access.


  1. 1.

    A. P. Soldatov, Douglis Analytic Functions [in Russian], Veliky Novgorod (1995).

  2. 2.

    A. P. Soldatov, “The Schwarz problem for Douglis analytic functions,” J. Math. Sci., New York 173, No. 2, 221–224 (2011).

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    V. G. Nikolaev and A. P. Soldatov, “On the solution of the Schwarz problem for J-analytic functions in a domain bounded by a Lyapunov contour” Differ. Equ. 51, No. 7, 962–966 (2015).

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    I. I. Privalov, Introduction to the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  5. 5.

    N. I. Muskhelishvili, Singular Integral Equations, Wolters-Noordhoff Publishing, Groningen (1967).

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to V. G. Nikolaev.

Additional information

Translated from Problemy Matematicheskogo Analiza 90, January 2018, pp. 63-72.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Nikolaev, V.G. On Solutions to the Schwarz Problem in a Disk in the Three-Dimensional Case. J Math Sci 228, 672–683 (2018). https://doi.org/10.1007/s10958-017-3655-2

Download citation