## Abstract

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.

Show Summary Details# Infinite dimension of solutions
of the Dirichlet problem

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*Journal of Mathematical Sciences*, 2017, Volume 221, Number 5, Page 638*Reports of the National Academy of Sciences of Ukraine*, 2016, Number 2, Page 13*Analysis and Mathematical Physics*, 2017, Volume 7, Number 3, Page 285*Journal of Mathematical Sciences*, 2016, Volume 214, Number 2, Page 200

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### formerly Central European Journal of Mathematics

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Vladimir Ryazanov

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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**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.

©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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