We are dedicated to addressing Riemann–Hilbert boundary value problems (RHBVPs) with variable coefficients, where the solutions are valued in the Clifford algebra of \(\mathbb {R}_{0,n}\), for biaxially monogenic functions defined in the biaxially symmetric domains of the Euclidean space \(\mathbb {R}^{n}\). Our research establishes the equivalence between RHBVPs for biaxially monogenic functions defined in biaxially domains and RHBVPs for generalized analytic functions on the complex plane. We derive explicit solutions and conditions for solvability of RHBVPs for biaxially monogenic functions. Additionally, we explore related Schwarz problems and RHBVPs for biaxially meta-monogenic functions.

我们致力于解决具有可变系数的黎曼-希尔伯特边值问题 （RHBVP），其中解在 \（\mathbb {R}_{0，n}\） 的克利福德代数中计算，用于欧几里得空间 \（\mathbb {R}^{n}\） 中定义的双轴单基因函数。我们的研究确定了在双轴域中定义的双轴单基因函数的 RHBVPs 与复平面上广义解析函数的 RHBVPs 之间的等效性。我们推导出了 RHBVPs 的双轴单基因功能的可解性的明确解决方案和条件。此外，我们还探讨了相关的 Schwarz 问题和双轴元单基因功能的 RHBVP。