Robin boundary-value problem for the Beltrami equation

  • I. Gençtürk Kırıkkale University, Turkey
Keywords: Beltrami equation, Robin boundary value problem, singular integral operator

Abstract

UDC 517.5

We investigate the unique solution of the Robin boundary-value problem for the Beltrami equation with constant coefficients in the unit disc by using a technique based on a singular integral operator defined on $ L_{p}(\mathbb{D})$ for all $p>2.$

References

H. Begehr, Complex analytic methods for partial differential equations: an introductory text, World Sci. (1994). DOI: https://doi.org/10.1142/2162

H. Begehr, Boundary value problems in complex analysis, I, Bol. Asoc. Mat. Venez., 12, 65–85 (2005).

H. Begehr, G. Harutjunjan, Robin boundary value problem for the Cauchy–Riemann operator, Complex Var. and Elliptic Equat., 50, № 15, 1125–1136 (2005). DOI: https://doi.org/10.1080/02781070500327832

H. Begehr, G. Harutjunjan, Robin boundary value problem for the Poisson equation, J. Anal. and Appl., 4, № 3, 201–213 (2006).

H. Begehr, G. Harutjunjan, Neumann problem for the Beltrami operator and for second order operators with Poisson–Bitsadze operator as main part, Complex Var. and Elliptic Equat., 54, № 12, 1129–1150 (2009). DOI: https://doi.org/10.1080/17476930903276084

H. Begehr, E. Obolashvili, Some boundary value problems for a Beltrami equation, Complex Var. and Elliptic Equat., 26, № 1-2, 113–122 (1994). DOI: https://doi.org/10.1080/17476939408814769

G. Harutyunyan, Boundary value problems for the Beltrami operator, Complex Var. and Elliptic Equat., 52, № 6, 475–484 (2007). DOI: https://doi.org/10.1080/17476930701200922

D. A. Kovtonyuk, I. V. Petkov, V. I. Ryazanov, R. Salimov, Boundary behavior and the Dirichlet problem for Beltrami equations, St. Petersburg Math. J., 25, № 4, 587–603 (2014). DOI: https://doi.org/10.1090/S1061-0022-2014-01308-8

D. A. Kovtonyuk, I. V. Petkov, V. I. Ryazanov, R. Salimov, On the Dirichlet problem for the Beltrami equation, J. Anal. Math., 122, № 1, 113–141 (2014). DOI: https://doi.org/10.1007/s11854-014-0005-x

I. N. Vekua, Generalized analytic functions, Pergamon, Oxford (1962).

Published
10.05.2023
How to Cite
Gençtürk, I. “Robin Boundary-Value Problem for the Beltrami Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 4, May 2023, pp. 447 -54, doi:10.37863/umzh.v75i4.6838.
Section
Research articles