Homogeneous Hilbert boundary-value problem with several points of turbulence
- Authors: Fatykhov A.K.1, Salimov R.B.1, Shabalin P.L.1
-
Affiliations:
- Kazan State University of Architecture and Engineering
- Issue: Vol 38, No 3 (2017)
- Pages: 414-419
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199195
- DOI: https://doi.org/10.1134/S199508021703009X
- ID: 199195
Cite item
Abstract
We consider Riemann–Hilbert boundary value problem with infinite index in unit disk. Its coefficient is Hölder-continuous everywhere on the unit circle excluding a finite set of points, where its argument has power discontinuities of order less one. The present article is the first research of this version of Hilbert boundary-value problem with infinite index. We obtain formulas for its general solution, investigate existence ad uniqueness of solutions, and describe the set of solutions in the case of non-uniqueness. Our technique is based on theory of entire functions and geometric theory of functions.
About the authors
A. Kh. Fatykhov
Kazan State University of Architecture and Engineering
Author for correspondence.
Email: vitofat@gmail.com
Russian Federation, ul. Zelenaya 1, Kazan, 420043
R. B. Salimov
Kazan State University of Architecture and Engineering
Email: vitofat@gmail.com
Russian Federation, ul. Zelenaya 1, Kazan, 420043
P. L. Shabalin
Kazan State University of Architecture and Engineering
Email: vitofat@gmail.com
Russian Federation, ul. Zelenaya 1, Kazan, 420043
![](/img/style/loading.gif)