Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries

@article{Akman2015RectifiabilityAE,
  title={Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries},
  author={M. Akman and M. Badger and S. Hofmann and Jos'e Mar'ia Martell},
  journal={arXiv: Classical Analysis and ODEs},
  year={2015}
}
  • M. Akman, M. Badger, +1 author Jos'e Mar'ia Martell
  • Published 2015
  • Mathematics
  • arXiv: Classical Analysis and ODEs
  • Let $\Omega \subset \mathbb{R}^{n+1}$, $n\geq 2$, be 1-sided NTA domain (aka uniform domain), i.e. a domain which satisfies interior Corkscrew and Harnack Chain conditions, and assume that $\partial\Omega$ is $n$-dimensional Ahlfors-David regular. We characterize the rectifiability of $\partial\Omega$ in terms of the absolute continuity of surface measure with respect to harmonic measure. We also show that these are equivalent to the fact that $\partial\Omega$ can be covered $\mathcal{H}^n$-a.e… CONTINUE READING
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