Boundary value problem with an oblique derivative for uniformly elliptic operators with discontinuous coefficients

Strong solvability is proved in the Sobolev space W-2,W-p(Omega), 1 < p < infinity, for the regular oblique derivative problem Sigma(i)(j)(n)= 1 a(ij) (x) D(ij)u + Sigma(i)(n) = (1)b(i) (x) D(i)u + c(x)u = f(x) a.e. Omega, partial derivative u/partial derivative l + sigma (x) u = phi (x) on partial derivative Omega, assuming a(ij) is an element of VMO boolean AND L-infinity (Omega), b(i), c is an element of L-q (Omega), c less than or equal to 0, sigma less than or equal to 0.