Riemann–Hilbert problems for null-solutions to iterated generalized Cauchy–Riemann equations in axially symmetric domains. (May 2016)

• Record Type: Journal Article
• Authors: He, Fuli; Ku, Min; Kähler, Uwe; Sommen, Frank; Bernstein, Swanhild
• Is Part Of: Computers & mathematics with applications. Volume 71:issue 10(2016)
• Page Start: 1990
• Page End: 2000
• Publication Date: 2016-05
• Subjects: Quaternion analysis -- Iterated generalized Cauchy–Riemann operator -- Axial symmetry -- Riemann–Hilbert problems -- Variable coefficients; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.03.017
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We consider Riemann–Hilbert boundary value problems (for short RHBVPs) with variable coefficients for axially symmetric poly-monogenic functions, i.e., null-solutions to iterated generalized Cauchy–Riemann equations, defined in axially symmetric domains. This extends our recent results about RHBVPs with variable coefficients for axially symmetric monogenic functions defined in four-dimensional axially symmetric domains. First, we construct the Almansi-type decomposition theorems for poly-monogenic functions of axial type. Then, making full use of them, we give the integral representation solutions to the RHBVP considered. As a special case, we derive solutions to the corresponding Schwarz problem. Finally, we generalize the result obtained to functions of axial type which are null-solutions to perturbed iterated generalized Cauchy–Riemann equations D α k ϕ = 0, k ⩾ 2 ( k ∈ N ), α ∈ R .