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Open Mathematics

formerly Central European Journal of Mathematics

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

1 Issue per year


IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

CiteScore 2016: 0.62

SCImago Journal Rank (SJR) 2016: 0.454
Source Normalized Impact per Paper (SNIP) 2016: 0.850

Mathematical Citation Quotient (MCQ) 2016: 0.23

Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1 (May 2015)

Issues

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:
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Published Online: 2015-05-20 | DOI: https://doi.org/10.1515/math-2015-0034

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.

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

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

References

  • [1] Dovgoshey O., Martio O., Ryazanov V., Vuorinen M. The Cantor function, Expo. Math., 2006, 24, 1-37 Google Scholar

  • [2] Efimushkin A., Ryazanov V. On the Riemann-Hilbert problem for the Beltrami equations, Contemporary Mathematics (to appear), see also preprint http://arxiv.org/abs/1402.1111v3 [math.CV] 30 July 2014, 1-25 Google Scholar

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

  • [4] Gehring F.W., On the Dirichlet problem, Michigan Math. J., 1955-1956, 3, 201 Google Scholar

  • [5] Goluzin G.M., Geometric theory of functions of a complex variable, Transl. of Math. Monographs, 26, American Mathematical Society, Providence, R.I., 1969 Google Scholar

  • [6] Koosis P., Introduction to Hp spaces, 2nd ed., Cambridge Tracts in Mathematics, 115, Cambridge Univ. Press, Cambridge, 1998 Google Scholar

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

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.

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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

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Vladimir Ya. Gutlyanskiĭ and Vladimir I. Ryazanov
Journal of Mathematical Sciences, 2017, Volume 221, Number 5, Page 638
[2]
A.S. Yefimushkin and V.I. Ryazanov
Reports of the National Academy of Sciences of Ukraine, 2016, Number 2, Page 13
[3]
Vladimir Ryazanov
Analysis and Mathematical Physics, 2017, Volume 7, Number 3, Page 285
[4]
Vladimir Gutlyanskii, Vladimir Ryazanov, and Artem Yefimushkin
Journal of Mathematical Sciences, 2016, Volume 214, Number 2, Page 200

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