Abstract
The conformal mapping of the square with circular disjoint holes onto the square with disjoint slits is constructed. This conformal mapping is considered as a solution of the Riemann–Hilbert problem for a multiply connected domain in a class of double periodic functions. The problem is solved by reduction to a system of functional equations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
L. Berlyand, V.V. Mityushev, Generalized Clausius-Mossotti formula for random composite with circular Fibers. J. Stat. Phys. 102, 481–509 (2001)
R. Czapla, V.V. Mityushev, N. Rylko, Conformal mapping of circular multiply connected domains onto segment domains. Electron. Trans. Numer. Anal. 39, 286–297 (2012)
T.K. DeLillo, T.A. Driscoll, A.R Elcrat, J.A. Pfaltzgraff, Radial and circular slit maps of unbounded multiply connected circle domains. Proc. R. Soc. A 464, 1719–1737 (2008)
V.V. Mityushev, On the solutions of the \(\mathbb{R}\)-linear boundary value problem (Markushevich’s problem) on the torus and cylinder. Izv. vuzov. Math. Preprint N 7546-B87, VINITI (1987). http://mityu.up.krakow.pl/static/papers/1987-VINITI.PDF
V. Mityushev, Steady heat conduction of the material with an array of cylindrical holes in the non-linear case. IMA J Appl. Math. 61, 91–102 (1998)
V.V. Mityushev, Riemann–Hilbert problems for multiply connected domains and circular slit maps. Comput. Methods Funct. Theory 11, 575–590 (2011)
V.V. Mityushev, Schwarz–Christoffel formula for multiply connected domains. Comput. Methods Funct. Theory 12, 449–463 (2012)
V. Mityushev, Poincaré \(\boldsymbol{\alpha }\)-series for classical Schottky groups and its applications, in Analytic Number Theory, Approximation Theory, and Special Functions, ed. by G.V. Milovanovi, M.T. Rassias (Springer, Berlin, 2014), pp. 827–852
V. Mityushev, P.M. Adler, Darcy flow around a two-dimensional lens, J. Phys. A Math. Gen. 39, 3545–3560 (2006)
V.V. Mityushev, S.V. Rogosin, Constructive Methods for Linear and Non-linear Boundary Value Problems of the Analytic Function. Theory and Applications (Chapman & Hall/CRC, Boca Raton, 2000)
A. Weil, Elliptic Functions According to Eisenstein and Kronecker (Springer, Berlin, 1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Czapla, R., Mityushev, V.V. (2017). Conformal Mapping of Circular Multiply Connected Domains Onto Domains with Slits. In: Dang, P., Ku, M., Qian, T., Rodino, L. (eds) New Trends in Analysis and Interdisciplinary Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-48812-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-48812-7_3
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-48810-3
Online ISBN: 978-3-319-48812-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)