$$ \bar{\partial } $$ and $$ {\bar{\partial }_b} $$ Problems on Nonsmooth Domains

Abstract

In this survey article we want to describe our method for constructing barriers on weakly pseudoconvex domains with smooth boundaries and give some applications to nonsmooth pseudoconvex domains. We also consider annuli of a very general type which are difference sets of a large piecewise smooth pseudoconvex domain with a union of piecewise smooth pseudoconvex domains in the interior. We do not impose any further conditions on the Levi form. For more details on the proofs, see the papers [24], [27], [28], [29].