Abstract
We establish a connection between the absolute continuity of elliptic measure associated with a second order divergence form operator with bounded measurable coefficients with the solvability of an end-point BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies L p solvability for all p>p 0.
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Communicated by Marco Peloso.
Research of M. Dindos was supported by EPRC grant EP/F014589/1-253000.
Research of C. Kenig and J. Pipher was supported by NSF.
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Dindos, M., Kenig, C. & Pipher, J. BMO Solvability and the A ∞ Condition for Elliptic Operators. J Geom Anal 21, 78–95 (2011). https://doi.org/10.1007/s12220-010-9142-3
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DOI: https://doi.org/10.1007/s12220-010-9142-3