TheLpDirichlet Problem for Divergence Form Elliptic Operators with Non-smooth Coefficients

We present conditions on the disagreement between two elliptic operators which ensure the preservation ofLpsolvability for the Dirichlet problem on the unit ball in Rn. The conditions depend onpand differ from previous results on this question. Furthermore, the conditions are sharp in the sense that they are equivalent toLpsolvability for a special class of operators which arise in then=2 case.