Jan Maly, David Swanson, William P. Ziemer
Published 2001-12-01Version 1
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 Lorentz space $L^{m,1}(R^n)$. This is accomplished by showing that the graph of $f$ in $R^{n+m}$ is a Hausdorff $n$-rectifiable set.
Comments: Submitted for publication, 16 pages
On orders of approximation functions of generalized smoothness in Lorentz spaces
Boundary blow up under Sobolev mappings
On embedding of Besov spaces of zero smoothness into Lorentz spaces
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