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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 13, Issue 1 (May 2015)


Infinite dimension of solutions of the Dirichlet problem

Vladimir Ryazanov
  • Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 74 Roze Luxemburg Str., 83114, Donetsk, Ukraine
Published Online: 2015-05-20 | DOI: https://doi.org/10.1515/math-2015-0034


It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.

Keywords: Dirichlet problem; Harmonic functions; Laplace equation; Riemann-Hilbert problem

MSC: 31A05, 31A20, 31A25, 31B25, 35Q15, 30E25, 31C05, 34M50, 35F45


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  • [3] Garnett J.B., Marshall D.E. Harmonic Measure, Cambridge Univ. Press, Cambridge, 2005

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  • [7] Ryazanov V., On the Riemann-Hilbert Problem without Index, Ann. Univ. Bucharest, Ser. Math. 2014, 5, 169-178

About the article

Received: 2014-10-29

Accepted: 2014-05-10

Published Online: 2015-05-20

Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0034. Export Citation

©2015 Vladimir Ryazanov. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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