Necessary and sufficient conditions for the chain rule in W 1 , 1 loc ( R N ; R d ) and BV loc ( R N ; R d )

@inproceedings{Leoni2005NecessaryAS,
  title={Necessary and sufficient conditions for the chain rule in W 1 , 1 loc ( R N ; R d ) and BV loc ( R N ; R d )},
  author={Gualtiero Leoni and Massimiliano Morini},
  year={2005}
}
In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space W 1,1 loc ( R ;R ) and in the space of functions of bounded variation BVloc ( R ;R ) . 

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