On L-P-estimates of optimal type for the parabolic oblique derivative problem with VMO-coefficients - A refined version

We prove W-p(2,1)(Omega(T))-estimates (1 < p < infinity) for parabolic operators with a second-order elliptic part in non-divergence form with essentially bounded VMO-coefficients. The boundary condition Sigma(n)(i)(=1) b(i)(xi, t)partial derivative(i)u(xi, t) = g(xi,t) on partial derivative Omega T is considered in the non-degenerate case, and the b(i) are only assumed to be in space-time Sobolev-spaces (see condition (B)).