Abstract
The Riemann–Hilbert boundary value problems with Clifford-algebra valued variable coefficients for null-solutions to iterated generalised Cauchy–Riemann equations, which are also so-called poly-monogenic functions, defined over axial symmetric domains of \(\mathbb {R}^{n+1}\), are studied in this context. The integral representation solutions to such problems and their solvable conditions are given. Here, the idea of ours is to use the Fischer decomposition theorems for poly-monogenic functions considered. As an application, the solutions to a Schwarz problem are derived too. Then, the results obtained are extended to axially symmetric null-solutions to perturbed iterated generalised Cauchy–Riemann equations.
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This work was supported by National Natural Science Foundation of China (11601525).
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He, F., Huang, Q. & Ku, M. Riemann–Hilbert Problems for Axially Symmetric Null-Solutions to Iterated Generalised Cauchy–Riemann Equations in \(\mathbb {R}^{n+1}\). J Geom Anal 34, 57 (2024). https://doi.org/10.1007/s12220-023-01509-1
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DOI: https://doi.org/10.1007/s12220-023-01509-1
Keywords
- Riemann–Hilbert problem
- Generalised Cauchy–Riemann operator
- Generalised analytic function
- Clifford algebra