Calculus of Variations and Geometric Measure Theory

G. Leoni - M. Morini

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

created by leoni on 10 Jan 2005
modified by morini on 17 Sep 2007


Published Paper

Inserted: 10 jan 2005
Last Updated: 17 sep 2007

Journal: J. Eur. Math. Soc. (JEMS)
Volume: 9
Number: 2
Pages: 219-252
Year: 2007


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 $BV_{loc}(R^N;R^d)$.