Hypoellipticity of the $\bar{\partial }$-Neumann problem at exponentially degenerate points

Abstract

We prove that the $\bar{\partial }$-Neumann solution operator is locally regular in a domain which has compactness estimates, is of finite type outside a curve transversal to the CR directions and for which the holomorphic tangential derivatives of a defining function are subelliptic multipliers in the sense of Kohn.

arXiv comment11 pages. Revision of arxiv 10040919v1, April 6 2010