论文标题
在$（φ，ψ）$的Riemann-Hilbert边界价值问题上 - $ \ Mathbb {r}^m $中的谐波函数
On a Riemann-Hilbert boundary value problem for $(φ,ψ)$-harmonic functions in $\mathbb{R}^m$
论文作者
论文摘要
本文的目的是解决$（φ，ψ）$ - 谐波函数的一种Riemann-Hilbert边界价值问题，该问题与使用欧几里得空间的两个正交基础$ \ Mathbb {r}^m $相关。我们使用Clifford分析的语言解决了这个问题，以在Jordan域$ω\ subset \ Mathbb {r}^m $带有分形边界中获得问题的明确表达。这项研究中的显着特征之一是边界数据涉及高级Lipschitz的功能类别。
The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for $(φ,ψ)$-harmonic functions, which are linked with the use of two orthogonal basis of the Euclidean space $\mathbb{R}^m$. We approach this problem using the language of Clifford analysis for obtaining the explicit expression of the solution of the problem in a Jordan domain $Ω\subset\mathbb{R}^m$ with fractal boundary. One of the remarkable feature in this study is that the boundary data involves higher order Lipschitz class of functions.
