Neutral Poincaré problem in L^p-Sobolev spaces: Regularity and Fredholmness

We are dealing with the degenerate oblique derivative problem for uniformly elliptic operators with low regular coefficients in the framework of Sobolev's classes W-2,W-p(Omega) for any p > 1. The boundary operator is prescribed in terms of a directional derivative with respect to a vector field l that becomes tangential to partial derivative Omega at the points of a nonempty set epsilon subset of partial derivative Omega and is directed outward Omega on partial derivative Omega\epsilon. The results of Maugeri, Palagachev, and Vitanza (2001) on strong solvability, uniqueness, and regularity are improved. Moreover, we show that the problem under consideration is of Fredholm type with index zero.