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Publication 05-CNA-01

Necessary and sufficient conditions for the chain rule in $W_{loc}^{1,1}(R^N;R^d)$ and $BV_{loc}(R^N;R^d)$

Giovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

and

Massimiliano Morini
SISSA/ISAS
via Beirut 4
340 14 Trieste
ITALY

Abstract: In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space $W_{loc}^{1,1}(R^N;R^d)$ and in the space of functions of bounded variation $BV_{loc}(R^N;R^d)$ .

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