Abstract
In this_paper we prove that locally there is no obstruction to global regularity for the 9-Neumann problem. By this we mean the following: Let D be a smoothly bounded pseudoconvex domain in C n , n ≥ 2, and let p ∈ D. Given any m ∈ Z + , one can construct a smoothly bounded pseudoconvex subdomain D m ⊆ D such that bD m ∩ bD contains an open neighborhood of p in bD and the d -Neumann problem on D m is globally regular up to order m in the sense of the Sobolev norm. © 1991 American Mathematical Society.