Riemann-Hilbert-type Boundary Value Problems on a Half Hexagon

Riemann-Hilbert-type Boundary Value Problems on a Half Hexagon

In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann-Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed. Finally, we inves...

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Veröffentlicht in:Acta mathematica Sinica. English series 2017-09, Vol.33 (9), p.1249-1266
Hauptverfasser: Akel, Mohamed, Alabbad, Fatimah
Format: Artikel
Sprache:eng
Schlagworte:
Boundary value problems
Cauchy-Riemann equations
Hilbert space
Integrals
Mathematics
Mathematics and Statistics
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Zusammenfassung:In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann-Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed. Finally, we investigate the Schwarz problem and the Riemann-Hilbert problem for inhomogeneous Cauchy-Riemann equations.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-6127-6