Square Functions and the $A_\infty$ Property of Elliptic Measures

C. Kenig, B. Kirchheim, J. Pipher, T. Toro

Published 2014-09-25Version 1

In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric divergence form operators. We show that a certain optimal Carleson measure estimate for bounded solutions of such operators implies a regularity result for the associated elliptic measure.