We study the unique solution of the Robin boundary-value problem for the Beltrami equation with constant coefficients in a unit disc by using a technique based on a singular integral operator defined on Lp(đť”») for all p > 2.
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References
H. Begehr, Complex Analytic Methods for Partial Differential Equations: an Introductory Text, World Scientific Publ., River Edge, NJ (1994).
H. Begehr, “Boundary value problems in complex analysis, I,” Bol. Asoc. Mat. Venez., 12, 65–85 (2005).
H. Begehr and G. Harutjunjan, “Robin boundary value problem for the Cauchy–Riemann operator,” Complex Var. Elliptic Equat., 50, No. 15, 1125–1136 (2005).
H. Begehr and G. Harutjunjan, “Robin boundary value problem for the Poisson equation,” J. Anal. Appl., 4, No. 3, 201–213 (2006).
H. Begehr and G. Harutjunjan, “Neumann problem for the Beltrami operator and for second order operators with Poisson–Bitsadze operator as main part,” Complex Var. Elliptic Equat., 54, No. 12, 1129–1150 (2009).
H. Begehr and E. Obolashvili, “Some boundary value problems for a Beltrami equation,” Complex Var. Elliptic Equat., 26, No. 1-2, 113–122 (1994).
G. Harutyunyan, “Boundary value problems for the Beltrami operator,” Complex Var. Elliptic Equat., 52, No. 6, 475–484 (2007).
D. A. Kovtonyuk, I. V. Petkov, V. I. Ryazanov, and R. Salimov, “Boundary behavior and the Dirichlet problem for Beltrami equations,” St. Petersburg Math. J., 25, No. 4, 587–603 (2014).
D. A. Kovtonyuk, I. V. Petkov, V. I. Ryazanov, and R. Salimov, “On the Dirichlet problem for the Beltrami equation,” J. Anal. Math., 122, No. 1, 113–141 (2014).
I. N. Vekua, Generalized Analytic Functions, Pergamon Press, London–Paris–Frankfurt; Addison-Wesley, Reading, Mass. (1962).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 4, pp. 447–454, April, 2023. Ukrainian DOI: 10.37863/umzh.v75i4.6838.
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Gençtürk, İ. Robin Boundary-Value Problem for the Beltrami Equation. Ukr Math J 75, 510–518 (2023). https://doi.org/10.1007/s11253-023-02213-7
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DOI: https://doi.org/10.1007/s11253-023-02213-7