\(C^ k\)-regularity for the \({\bar \partial}\)-equation on strictly pseudoconvex domains with piecewise smooth boundaries
type: Item
instance of: scholarly article
title: \(C^ k\)-regularity for the \({\bar \partial}\)-equation on strictly pseudoconvex domains with piecewise smooth boundaries
zbMATH Open document ID: 0673.32019
DOI: 10.1007/BF02570747
author: Joachim Michel
author: Alessandro Perotti
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174138
review text: The authors study the equation \({\bar \partial}u=f\) on a piecewise strictly pseudoconvex domain in \({\mathbb{C}}^ n\). A linear solution operator \(T^*_ q\) was given, such that, if f is a \({\bar\partial}\)-closed q-form, which is \({\mathcal C}^ k\)-regular up to the boundary, \(T^*_ qf=u\) satisfies the following \({\mathcal C}^ k\)-estimates: \[ \| u\|_{{\mathcal C}^{k-\epsilon}}\leq const(k,\epsilon)\cdot \| f\|_{{\mathcal C}^ k} \] for arbitrary real numbers \(0<\epsilon\).
reviewed by: Joachim Michel
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 4101587
MaRDI profile type: Publication
cites work: Deformation of complex structures, estimates for the (partial d) equation, and stability of the Bergman kernel
cites work: Lösungsoperatoren für den Cauchy-Riemann-Komplex mit \(\mathcal C^K\)- Abschätzungen
cites work: Q1821916
description: scientific article; zbMATH DE number 4101587