Publication at Faculty of Mathematics and Physics |
2010
Abstract
Let $p\geq n-1$ and suppose that $f:\Omega\to\rn$ is a homeomorphism in the Sobolev space $W^{1,p}_{\loc}(\Omega,\rn)$. Further let $u\in W^{1,q}_{\loc}(\Omega)$ where $q=\frac{p}{p-(n-1)}$ and for $q>n$ we also assume that $u$ is continuous.
Then $u\circ f^{-1}\in BV_{\loc}(f(\Omega))$ and if we moreover assume that $f$ is a mapping of finite distortion, then $u\circ f^{-1}\in W^{1,1}_{\loc}(f(\Omega))$.