数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (4): 433-.
• 论文 • 下一篇
宋迎清, 扬孝平, 刘振海
SONG Ying-Qing, YANG Xiao-Beng, LIU Zhen-Hai
摘要：
The aim of this paper is to get the decomposition of distributional
derivatives of functions with bounded
variation in the framework of Carnot-Carath\'eodory
spaces (C-C spaces in brievity) in which the vector fields are of
Carnot type. For this purpose the approximate
continuity of BV functions is discussed first, then approximate
differentials of $ L^1$ functions are defined in the case that vector
fields are of Carnot type and finally the decomposition $Xu=\nabla u\cdot
L^n+X^su$ is proved, where $ u\in BV_X(\Omega)$ and $\nabla u$
denotes the approximate differential of $u$.
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