Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (4): 433-.

• Articles •     Next Articles

DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATH´|EODORY SPACES

 SONG Ying-Qing, YANG Xiao-Beng, LIU Zhen-Hai   

  1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
    2.Department of Mathematics, Hunan University of City, Yiyang 413000, China
    3.Department of Mathematics, Changsha University of Electrical Power, Changsha 410077, China
  • Online:2003-10-06 Published:2003-10-06
  • Supported by:

    This work is supported by NNSF of China (19771048)

Abstract:

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 $u$.

Key words: BV function, C-C space, Radon measure, vector field, approximate differen-
tial

CLC Number: 

  • 26A45
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