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Area, coarea, and approximation in$W$^{1,1}

David Swanson Department of Mathematics, University of Louisville

TBD mathscidoc:1701.333115

Arkiv for Matematik, 45, (2), 381-399, 2005.12
Let Ω⊂ℝ^{$n$}be an arbitrary open set. We characterize the space$W$^{1,1}_{loc}(Ω) using variants of the classical area and coarea formulas. We use these characterizations to obtain a norm approximation and trace theorems for functions in the space$W$^{1,1}(ℝ^{$n$}).
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@inproceedings{david2005area,,
  title={Area, coarea, and approximation in$W$^{1,1}},
  author={David Swanson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620972096924},
  booktitle={Arkiv for Matematik},
  volume={45},
  number={2},
  pages={381-399},
  year={2005},
}
David Swanson. Area, coarea, and approximation in$W$^{1,1}. 2005. Vol. 45. In Arkiv for Matematik. pp.381-399. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620972096924.
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