Riemann-Hilbert problems for null-solutions to iterated generalized Cauchy-Riemann equation on upper half ball
Riemann-Hilbert problems for null-solutions to iterated generalized Cauchy-Riemann equation on upper half ball
复制标题
上半球迭代广义柯西-黎曼方程零解的黎曼-希尔伯特问题
DOI：
10.1080/17476933.2019.1664484
复制
发表时间：
2020
影响因子：
0.9
通讯作者：
He Xiuli
中科院分区：
文献类型：
--
作者：
Ku Min;He Fuli;He Xiuli
研究了四维欧氏空间中以原点为中心的上半单位球上的迭代广义Cauchy-Riemann方程的变系数Riemann-Hilbert边值问题的轴对称零解.首先，我们证明了迭代广义Cauchy-Riemann方程轴对称零解的Almansi型分解定理。然后，我们给出了四维欧氏空间中以原点为中心的上半单位球上迭代广义Cauchy-Riemann方程的轴对称零解的Riemann-Hilbert问题的积分表示解.特别地，我们得到了四维欧氏空间中以原点为中心的上半单位球上迭代广义Cauchy-Riemann方程的轴对称零解的施瓦茨问题的解.最后，我们将结果进一步推广到四维欧氏空间中以原点为中心的上半单位球上Dαkφ=0，k≥2（k∈N），α∈R的轴对称零解.
We study Riemann–Hilbert boundary value problems with variable coefficients for axially symmetric null-solutions to the iterated generalized Cauchy–Riemann equation, defined over the upper half unit ball centred at the origin in four-dimensional Euclidean space. First, we prove an Almansi-type decomposition theorem for axially symmetric null-solutions to the iterated generalized Cauchy–Riemann equation. Then, we give integral representation solutions to the Riemann–Hilbert problems for axially symmetric null-solutions to iterated generalized Cauchy–Riemann equation over the upper half unit ball centred at the origin in four-dimensional Euclidean space. In particular, we derive solutions to the Schwarz problem for axially symmetric null-solutions to iterated generalized Cauchy–Riemann equation over the upper half unit ball centred at the origin in four-dimensional Euclidean space. Finally, we further extend the results to axially symmetric null-solutions to Dαkφ=0,k≥2(k∈N),α∈R over the upper half unit ball centred at the origin in four-dimensional Euclidean space.