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

TL;DR

This paper proves local regularity of the $ar ext{-} abla$-Neumann problem in certain complex domains with specific geometric and analytic properties, including finite type conditions and subelliptic multipliers.

Contribution

It establishes hypoellipticity results for the $ar ext{-} abla$-Neumann problem at points with exponential degeneracy, extending previous regularity theories.

Findings

Solution operator is locally regular in specified domains.

Domains with finite type outside a transversal curve satisfy regularity.

Subelliptic multipliers facilitate hypoellipticity at 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.