Sobolev functions whose inner trace at the boundary is zero

David Swanson Department of Mathematics, Indiana University William P. Ziemer Department of Mathematics, Indiana University

TBD mathscidoc:1701.332922

Arkiv for Matematik, 37, (2), 373-380, 1997.12
Let Ω⊂$R$^{$n$}be an arbitrary open set. In this paper it is shown that if a Sobolev function$f$∈$W$^{1,$p$}(Ω) possesses a zero trace (in the sense of Lebesgue points) on ϖΩ, then$f$is weakly zero on ϖΩ in the sense that$f$∈$W$_{0}^{1,$p$}(Ω).
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@inproceedings{david1997sobolev,
  title={Sobolev functions whose inner trace at the boundary is zero},
  author={David Swanson, and William P. Ziemer},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203556783693731},
  booktitle={Arkiv for Matematik},
  volume={37},
  number={2},
  pages={373-380},
  year={1997},
}
David Swanson, and William P. Ziemer. Sobolev functions whose inner trace at the boundary is zero. 1997. Vol. 37. In Arkiv for Matematik. pp.373-380. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203556783693731.
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