Regularity at the boundary and tangential regularity of solutions of the Cauchy–Riemann system

Tran Vu Khanh and Giuseppe Zampieri

Vol. 265 (2013), No. 2, 491–498

DOI: 10.2140/pjm.2013.265.491

Abstract

For a pseudoconvex domain D ⊂ ℂⁿ, we prove the equivalence of the local hypoellipticity of the system (∂,∂^∗) with the system (∂_b,∂_b^∗) induced at the boundary. This develops a former result of ours in which the theory of harmonic extension by Kohn was used. This technique is inadequate for the purpose of the present paper and must be replaced by that of the holomorphic extension.

Keywords

∂-Neumann problem, tangential ∂ system

Mathematical Subject Classification 2010

Primary: 32F10

Milestones

Received: 15 August 2012

Revised: 26 November 2012

Accepted: 10 December 2012

Published: 28 August 2013