The A∞ property of elliptic measures for operators with coefficients supported in Whitney-type cubes

It is proved the preservation of the A∞ property (with respect to surface measure) of harmonic measure associated to second order divergence form operators with bounded measurable coefficients, when the discrepancy between the main coefficients of the operators is supported on Whitney type rectangles of the unit ball of Rn. In particular neither the discrepancy between the coefficients satisfies a Carleson measure condition, nor the coefficients of the operators involved are radially independent, as in previous well known works. As an application of the perturbation result, we provide a class of operators with coefficients supported on Whitney type rectangles, for which the A∞ property holds.