Abstract
Let X be a Stein manifold of dimension n >= 3 Let Omega(1) be a weakly q-convex and Omega(2) be a weakly (n = q = 1)-convex in X with smooth boundaries such that (Omega) over bar (2) (sic) Omega(1) (sic) X Assume that Omega = Omega(1)\(Omega) over bar (2) In this paper, we establish sufficient conditions for the closed range of partial derivative on Omega. Moreover, we study the global boundary regularity of the partial derivative-problem on Omega.