Global analytic hypoellipticity of the \({\bar \partial}\)-Neumann problem on circular domains
type: Item
instance of: scholarly article
title: Global analytic hypoellipticity of the \({\bar \partial}\)-Neumann problem on circular domains
zbMATH Open document ID: 0621.35067
DOI: 10.1007/BF01393998
author: So-Chin Chen
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143564
review text: We show that if \(D\subset {\mathbb{C}}^ n\), \(n\geq 2\), is a smooth bounded pseudoconvex circular domain with real analytic defining function r(z) such that \(\sum ^{n}_{k=1}z_ k\partial r/\partial z_ k\neq 0\) for all z near the boundary, then the solution u to the \({\bar \partial}\)- Neumann problem, \[ \square u=(\overline{\partial \partial}^ *+{\bar \partial}^ *{\bar \partial})u=f, \] is real analytic up to the boundary, if the given form f is real analytic up to the boundary. In particular, if \(D\subset {\mathbb{C}}^ n\), \(n\geq 2\), is a smooth bounded complete Reinhardt pseudoconvex domain with real analytic boundary. Then \(\square\) is analytic hypoelliptic.
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4006838
zbMATH Keywords: pseudoconvex circular domain
zbMATH Keywords: real analytic defining function
zbMATH Keywords: \({\bar \partial }\)-Neumann problem
zbMATH Keywords: real analytic
zbMATH Keywords: complete Reinhardt pseudoconvex domain
zbMATH Keywords: analytic hypoelliptic
MaRDI profile type: Publication
cites work: Q3778256
cites work: Régularité pour \(\overline\partial\) dans quelques domaines faiblement pseudo-convexes
cites work: On the global real analyticity of solutions to the neumann problems
cites work: The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
cites work: Global analytic-hypoellipticity of the \(\overline\partial\)-Neumann problem
OpenAlex ID: W2052772837
description: scientific article; zbMATH DE number 4006838