Inserted: 3 nov 2011
Last Updated: 15 dec 2012
Journal: Manuscripta Math.
In this paper we consider the chain rule formula for compositions $x\mapsto F(x,u(x))$ in the case when $u$ has a Sobolev or $BV$ regularity and $F(x,z)$ is separately Sobolev, or $BV$, with respect to $x$ and $C^1$ with respect to $z$. Our results extend to this "nonautonomous" case the results known for compositions $x\mapsto F(u(x))$.
Keywords: Chain Rule, $BV$ functions