The coarea formula for Sobolev mappings

Jan Maly, David Swanson, William P. Ziemer

We extend Federer's coarea formula to mappings $f$ belonging to the Sobolev class $W^{1,p}(R^n;R^m)$, $1\le m<n$, $p>m$, and more generally, to mappings with gradient in the Lor…