Necessary and Sufficient Conditions for Absolute Continuity of Elliptic- Harmonic Measure

Our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding Poisson kernel for the Dirichlet problem exist. This condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7(t) satisfying the Dini-type condition