# BMO Solvability and Absolute Continuity of Harmonic Measure

@article{Hofmann2016BMOSA,
title={BMO Solvability and Absolute Continuity of Harmonic Measure},
author={Steve Hofmann and Phi Long Le},
journal={The Journal of Geometric Analysis},
year={2016},
volume={28},
pages={3278-3299}
}
• Published 1 July 2016
• Mathematics
• The Journal of Geometric Analysis
We show that for a uniformly elliptic divergence form operator L, defined in an open set $$\Omega$$Ω with Ahlfors–David regular boundary, BMO solvability implies scale-invariant quantitative absolute continuity (the weak-$$A_\infty$$A∞ property) of elliptic-harmonic measure with respect to surface measure on $$\partial \Omega$$∂Ω. We do not impose any connectivity hypothesis, qualitative, or quantitative; in particular, we do not assume the Harnack Chain condition, even within individual… Expand
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