On the Poincaré-Bogovski lemma on differential forms
type: Item
instance of: scholarly article
title: On the Poincaré-Bogovski lemma on differential forms
zbMATH Open document ID: 0749.58004
author: Shuji Takahashi
published in: Proceedings of the Japan Academy. Series A
publication date: 1992-06-28T00:00:00Z
review text: Let \(D\) be a bounded domain in \(\mathbb{R}^ n\). The author constructs an integral operator \(K\) such that \(d(K\omega)+K(d\omega)=\omega\) for every differential form \(\omega\) on \(D\), with the property: if \(\text{supp }\omega\subset D\cup\Gamma\) then \(\text{supp }K\omega\subset D\cup \Gamma\), \(\Gamma\) being an open subset of \(\partial D\). In addition, the operator \(K\) is bounded in \(L_ p\) Sobolev spaces.
Mathematics Subject Classification ID: 58A10
zbMATH DE Number: 37718
zbMATH Keywords: differential form
zbMATH Keywords: Poincaré Lemma
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
full work available at URL: pjaa.68.1
OpenAlex ID: W2071144805
Wikidata QID: Q124964373
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DOI: 10.3792/PJAA.68.1
description: scientific article; zbMATH DE number 37718