On \(L^ p\) and Hölder estimates for the \({\bar \partial}\)-Neumann problem on strongly pseudo-convex domains
type: Item
instance of: scholarly article
title: On \(L^ p\) and Hölder estimates for the \({\bar \partial}\)-Neumann problem on strongly pseudo-convex domains
zbMATH Open document ID: 0631.32016
DOI: 10.1007/BF01456976
author: Der-Chen Chang
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
review text: Let \(\Omega\) be an open, relatively compact subset in \({\mathbb{C}}^{n+1}\), and assume that the boundary of \(\Omega\), \(\partial \Omega\), is smooth and strongly pseudoconvex. Suppose \(\Omega\) has an arbitrary Hermitian metric. Consider the \({\bar \partial}\)-Neumann problem: Given a (0,1)- form f, find a (0,1)-form u such that \(\square u=({\bar \partial}{\bar \partial}^ *+{\bar \partial}^ *{\bar \partial})u=f\) with two boundary conditions: \(u \in domain ({\bar \partial}^ *),\) \({\bar \partial}u \in domain ({\bar \partial}^ *).\) In this paper, we can write down a parametrix \({\mathfrak N}\) for this problem as a product of some well-known operators plus a remainder type operator and then get the optimal estimates.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 4025828
zbMATH Keywords: \({\bar \partial }\)-Neumann problem
zbMATH Keywords: \(L^ p\) estimates
zbMATH Keywords: Hölder estimates
zbMATH Keywords: strongly pseudoconvex domains
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01456976
OpenAlex ID: W2086558918
description: scientific article; zbMATH DE number 4025828