# A nonautonomous chain rule in $W^{1,1}$ and in $BV$

created by ambrosio on 03 Nov 2011
modified by decicco on 15 Dec 2012

[BibTeX]

Accepted Paper

Inserted: 3 nov 2011
Last Updated: 15 dec 2012

Journal: Manuscripta Math.
Year: 2012

Abstract:

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 $x\mapsto F(u(x))$.

Tags: GeMeThNES
Keywords: Chain Rule, $BV$ functions