W^ {2,p}-a priori estimates for the neutral Poincaré problem

A degenerate oblique derivative problem is studied for uniformly elliptic operators with low regular coefficients in the framework of Sobolev's classes W-2,W-p(Omega) for arbitrary p > 1. The boundary operator is prescribed in terms of a directional derivative with respect to the vector field l that becomes tangential to partial derivative Omega at the points of some non-empty subset epsilon subset of partial derivative Omega and is directed outwards Omega on partial derivative Omega \ epsilon. Under quite general assumptions of the behaviour of l, we derive a priori estimates for the W-2,W-p(Omega)-strong solutions for any p is an element of (1, infinity).