论文标题
分形表面上矢量场的普遍分解。
Generalized Laplacian decomposition of vector fields on fractal surfaces
论文作者
论文摘要
我们考虑使用分形边界的$ \ mathbb {r}^{3} $的Jordan域上的广义Laplacian矢量字段的行为。我们的方法基于Teodorescu变换的属性和向量场的合适扩展。具体而言，本文分别解决了边界上Hölder连续矢量场（也称为重建问题）的分解问题，分别分别为域中的两个广义Laplacian矢量场和其封闭的补充。此外，还建立了边界上Hölder连续矢量场的条件是该域中广义拉普拉斯矢量场的痕迹。
We consider the behavior of generalized Laplacian vector fields on a Jordan domain of $\mathbb{R}^{3}$ with fractal boundary. Our approach is based on properties of the Teodorescu transform and suitable extension of the vector fields. Specifically, the present article addresses the decomposition problem of a Hölder continuous vector field on the boundary (also called reconstruction problem) into the sum of two generalized Laplacian vector fields in the domain and in the complement of its closure, respectively. In addition, conditions on a Hölder continuous vector field on the boundary to be the trace of a generalized Laplacian vector field in the domain are also established.
