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The coarea formula for Sobolev mappings

Jan Maly·David Swanson·William P. Ziemer
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Abstract

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.

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Jan Maly, David Swanson, William P. Ziemer. 2001-12-01. The coarea formula for Sobolev mappings. https://arxiv.org/abs/math/0112008

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