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arXiv · 1007.5496

BMO solvability and the $A_\infty$ condition for elliptic operators

Martin Dindos·Carlos Kenig·Jill Pipher
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Abstract

We establish a connection between the absolute continuity of elliptic measure associated to a second order divergence form operator with bounded measurable coefficients with the solvability of an endpoint $BMO$ 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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Martin Dindos, Carlos Kenig, Jill Pipher. 2010-07-30. BMO solvability and the $A_\infty$ condition for elliptic operators. https://arxiv.org/abs/1007.5496

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