论文标题
Riemann-Hilbert的问题，用于$ \ Mathbb {r}^{n+1} $中的轴向对称单基因函数
Riemann-Hilbert problems for axially symmetric monogenic functions in $\mathbb{R}^{n+1}$
论文作者
论文摘要
我们专注于clifford-algebra值的可变系数Riemann-Hilbert边界价值问题$ \ big {（} $ for Short Rhbvps $ \ big \ big {）} $用于轴上是单基因的函数，在Euclidean Space $ \ Mathbb {r}在VEKUA系统的帮助下，我们首先在轴向域中考虑的RHBVP与复杂平面上的广义分析函数的RHBVP之间建立一对一的对应关系。随后，我们通过获得后一种问题的解决方案和可解决的条件来解决以前的问题，以便自然地为相应的Schwarz问题提供解决方案。此外，我们还使用上述方法将轴向示例溶解至$ \ big {（} \ Mathcal {d}-α\ big {）} ϕ = 0，α\ in \ mathbb {r} $。
We focus on the Clifford-algebra valued variable coefficients Riemann-Hilbert boundary value problems $\big{(}$for short RHBVPs$\big{)}$ for axially monogenic functions on Euclidean space $\mathbb{R}^{n+1},n\in \mathbb{N}$. With the help of Vekua system, we first make one-to-one correspondence between the RHBVPs considered in axial domains and the RHBVPs of generalized analytic function on complex plane. Subsequently, we use it to solve the former problems, by obtaining the solutions and solvable conditions of the latter problems, so that we naturally get solutions to the corresponding Schwarz problems. In addition, we also use the above method to extend the case to RHBVPs for axially null-solutions to $\big{(}\mathcal{D}-α\big{)}ϕ=0,α\in\mathbb{R}$.
