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Riemann-Hilbert problems for monogenic functions in axially symmetric domains. (English) Zbl 1332.30079

Summary: We consider Riemann-Hilbert boundary value problems (for short RHBVPs) with variable coefficients for axially symmetric monogenic functions defined in axial symmetric domains. This is done by constructing a method to reduce the RHBVPs for axially symmetric monogenic functions defined in four-dimensional axial symmetric domains into the RHBVPs for analytic functions defined over the complex plane. Then we derive solutions to the corresponding Schwarz problem. Finally, we generalize the results obtained to null-solutions of \((\mathcal{D}-\alpha)\phi=0\), \(\alpha\in\mathbb{R}\), where \(\mathbb{R}\) denotes the field of real numbers.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
35J56 Boundary value problems for first-order elliptic systems
35J58 Boundary value problems for higher-order elliptic systems
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