Integrability of Green potentials in fractal domains

Kaj Nyström Department of Mathematics, University of Umeå

TBD mathscidoc:1701.332862

Arkiv for Matematik, 34, (2), 335-381, 1995.10
We prove$L$^{$q$}-inequalities for the gradient of the Green potential ($Gf$) in bounded, connected NTA-domains in$R$^{$n$},$n$≥2. These domains may have a highly non-rectifiable boundary and in the plane the set of all bounded simply connected NTA-domains coincides with the set of all quasidiscs. We get a restriction on the exponent$q$for which our inequalities are valid in terms of the validity of a reverse Hölder inequality for the Green function close to the boundary.
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@inproceedings{kaj1995integrability,
  title={Integrability of Green potentials in fractal domains},
  author={Kaj Nyström},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203549288282671},
  booktitle={Arkiv for Matematik},
  volume={34},
  number={2},
  pages={335-381},
  year={1995},
}
Kaj Nyström. Integrability of Green potentials in fractal domains. 1995. Vol. 34. In Arkiv for Matematik. pp.335-381. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203549288282671.
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