# 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={Murat Akman and Matthew Badger and Steve Hofmann and Jos'e Mar'ia Martell}, journal={arXiv: Classical Analysis and ODEs}, year={2015} }

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…

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