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arXiv · 1512.02839

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

Luigi Ambrosio·Graziano Crasta·Virginia De Cicco·Guido De Philippis
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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 $x\mapsto F(u(x))$.

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Luigi Ambrosio, Graziano Crasta, Virginia De Cicco, Guido De Philippis. 2015-12-09. A nonautonomous chain rule in $W^{1,p}$ and $BV$. https://doi.org/10.1007/s00229-012-0548-z

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