Failure of global regularity of ∂b on a convex domain with only one flat point

Filippo Tolli

Vol. 185 (1998), No. 2, 363–398

DOI: 10.2140/pjm.1998.185.363

Abstract

In this paper we exhibit a bounded domain in C² with real analytic boundary which is strictly convex except at one point and for which the ∂_b operator is not analytic hypoelliptic modulo its kernel.

The importance of such an example is twofold: First it shows that the theorem of Boas and Straube on global C^∞ regularity for ∂_b on convex domains cannot be extended to the analytic case; secondly it is the first example of non analytic hypoellipticity of ∂_b on a domain with isolated weakly pseudoconvex points in the boundary.

Milestones

Received: 30 January 1997

Published: 1 October 1998