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Eurasian Mathematical Journal, 2014, том 5, номер 4, страницы 6–24
(Mi emj171)
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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
Schwarz problem for first order elliptic systems in unbounded sectors
M. Akelab, H. Begehrc a Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsaa, 31982, P.O. Box 380, Saudi Arabia
b Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
c Mathematical Institute, Free University Berlin, Arnimallee 3, D-14195 Berlin, Germany
Аннотация:
In this article we deal with a Schwarz-type boundary value problem for both the inhomogeneous Cauchy–Riemann equation and the generalized Beltrami equation on an unbounded sector with angle $\vartheta=\pi/n$, $n\in\mathbb N$. By the method of plane parquetingreflection and the Cauchy–Pompeiu formula for the sector, the Schwarz–Poisson integral formula is obtained. We also investigate the boundary behaviour and the $C^\alpha$-property of a Schwarz-type as well as of a Pompeiu-type operator. The solution to the Schwarz problem of the Cauchy–Riemann equation is explicitly expressed. Sufficient conditions on the coefficients of the generalized Beltrami equation are obtained under which the corresponding system of integral equations is contractive. This proves the existence of a unique solution to the Schwarz problem of the generalized Beltrami equation.
Ключевые слова и фразы:
Cauchy–Pompeiu formula, Schwarz–Poisson formula, Cauchy–Riemann equation, generalized Beltrami equation, Schwarz problem, contractive mapping principle.
Поступила в редакцию: 27.03.2014
Образец цитирования:
M. Akel, H. Begehr, “Schwarz problem for first order elliptic systems in unbounded sectors”, Eurasian Math. J., 5:4 (2014), 6–24
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj171 https://www.mathnet.ru/rus/emj/v5/i4/p6
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Страница аннотации: | 280 | PDF полного текста: | 121 | Список литературы: | 41 |
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