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}
}
  • S. Hofmann, P. Le
  • 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
BMO Solvability and $$A_{\infty }$$A∞ Condition of the Elliptic Measures in Uniform Domains
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  • S. Hofmann
  • Mathematics
  • Acta Mathematica Sinica, English Series
  • 2019
It is a well-known folklore result that quantitative, scale invariant absolute continuity (more precisely, the weak-A∞ property) of harmonic measure with respect to surface measure, on the bound¬aryExpand
Uniform rectifiability, elliptic measure, square functions, and $\varepsilon$-approximability
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Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions
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