Infinite dimension of solutions of the Dirichlet problem
Open Mathematics (2015)
- Volume: 13, Issue: 1
- ISSN: 2391-5455
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topVladimir Ryazanov. "Infinite dimension of solutions of the Dirichlet problem." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/270934>.
@article{VladimirRyazanov2015,
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.},
author = {Vladimir Ryazanov},
journal = {Open Mathematics},
keywords = {Dirichlet problem; Harmonic functions; Laplace equation; Riemann-Hilbert problem},
language = {eng},
number = {1},
pages = {null},
title = {Infinite dimension of solutions of the Dirichlet problem},
url = {http://eudml.org/doc/270934},
volume = {13},
year = {2015},
}
TY - JOUR
AU - Vladimir Ryazanov
TI - Infinite dimension of solutions of the Dirichlet problem
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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.
LA - eng
KW - Dirichlet problem; Harmonic functions; Laplace equation; Riemann-Hilbert problem
UR - http://eudml.org/doc/270934
ER -
References
top- [1] Dovgoshey O., Martio O., Ryazanov V., Vuorinen M. The Cantor function, Expo. Math., 2006, 24, 1-37 Zbl1098.26006
- [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
- [3] Garnett J.B., Marshall D.E. Harmonic Measure, Cambridge Univ. Press, Cambridge, 2005
- [4] Gehring F.W., On the Dirichlet problem, Michigan Math. J., 1955-1956, 3, 201
- [5] Goluzin G.M., Geometric theory of functions of a complex variable, Transl. of Math. Monographs, 26, American Mathematical Society, Providence, R.I., 1969 Zbl0183.07502
- [6] Koosis P., Introduction to Hp spaces, 2nd ed., Cambridge Tracts in Mathematics, 115, Cambridge Univ. Press, Cambridge, 1998 Zbl1024.30001
- [7] Ryazanov V., On the Riemann-Hilbert Problem without Index, Ann. Univ. Bucharest, Ser. Math. 2014, 5, 169-178 Zbl1324.31002
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