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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


Volume 13 (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
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
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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About the article

Received: 2014-10-29

Accepted: 2014-05-10

Published Online: 2015-05-20

Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0034.

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

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