A Stampacchia-type inequality for a fourth-order elliptic operator on Kähler manifolds and applications
type: Item
instance of: scholarly article
title: A Stampacchia-type inequality for a fourth-order elliptic operator on Kähler manifolds and applications
zbMATH Open document ID: 1192.53068
DOI: 10.4171/RLM/565
author: Luca Lussardi
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2010-05-31T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: The author studies the relation between Aeppli groups \(\Lambda^{p,q}(X)\) and the groups \(H^{p,q}(X)\) of all global harmonic forms of bidegree \((p,q)\) on a connected complete Kähler manifold \(X\). Under a topological condition (satisfied for compact and Stein manifolds) it is proved that \(\Lambda^{p,q}(X)\) is isomorphic to \(H^{p,q}(X)\). The main tool in the proof is a suitable Hodge-Kodaira decomposition of \(W^{p,q}(X)\) the completion of \(D^{p,q}(X)\) the space of forms with compact support in \(X\). The proof of this requires an integral inequality of Stampacchia-type for a certain fourth-order elliptic operator. Both this inequality and the Hodge-Kodaira decomposition hold independently of the topological assumption.
reviewed by: Gabriela Paola Ovando
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 14F25
zbMATH DE Number: 5714229
zbMATH Keywords: harmonic forms
zbMATH Keywords: Aeppli groups
zbMATH Keywords: Stampacchia-type inequality
zbMATH Keywords: Hodge-Kodaira decomposition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5714229