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Equivalent norms for the Sobolev space$W$_{0}^{$m,p$}(Ω)

Andreas Wannebo Department of Mathematics, The Royal Institute of Technology

TBD mathscidoc:1701.332814

Arkiv for Matematik, 32, (1), 245-254, 1993.2
A new proof is given for a theorem by V. G. Maz'ya. It gives a necessary and sufficient condition on the open set Ω in$R$^{$N$}for the functions in$W$_{0}^{$m,p$}(Ω) to have the ordinary norm equivalent to the norm obtained when including only the highest order derivatives in the definition. The proof is based on a kind of polynomial capacities, Maz'ya capacities.
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@inproceedings{andreas1993equivalent,
  title={Equivalent norms for the Sobolev space$W$_{0}^{$m,p$}(Ω)},
  author={Andreas Wannebo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203543190850623},
  booktitle={Arkiv for Matematik},
  volume={32},
  number={1},
  pages={245-254},
  year={1993},
}
Andreas Wannebo. Equivalent norms for the Sobolev space$W$_{0}^{$m,p$}(Ω). 1993. Vol. 32. In Arkiv for Matematik. pp.245-254. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203543190850623.
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