A computation of Green functions for the weighted biharmonic operators \(\Delta| z| ^{-2\alpha}\Delta\), with \(\alpha > -1\)
type: Item
instance of: scholarly article
title: A computation of Green functions for the weighted biharmonic operators \(\Delta| z| ^{-2\alpha}\Delta\), with \(\alpha > -1\)
zbMATH Open document ID: 0813.31001
DOI: 10.1215/S0012-7094-94-07502-9
published in: Duke Mathematical Journal
publication date: 1995-06-11T00:00:00Z
review text: Ayant précisé le domaine de définition de l'opérateur \(\Delta(| z|^{-2 \alpha} \Delta)\) sur le disque-unité \(D\), on montre qu'une fonction appartenant à ce domaine, au noyau de l'opérateur, et à \({\mathcal C}^ 1(\overline D \backslash \{0\})\), qui s'annule ainsi que son gradient à la frontière de \(D\), est la constante 0. On détermine ainsi de façon unique une fonction de Green \(U_ \alpha\), que l'on calcule explicitement pour \(\alpha\) entier; pour \(\alpha\) non entier, \(U_ \alpha\) est donnée par une formule intégrale où figure la fonction de Green de \(\Delta\) sur \(D\), et peut aussi s'exprimer à l'aide de la fonction de Green de \(\Delta (e^{2Im z} \Delta)\) sur le demi-plan \(\text{Im } z>0\).
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 706706
zbMATH Keywords: weighted biharmonic operator
zbMATH Keywords: Green's function
author: Håkan Hedenmalm
reviewed by: Rose-Marie Hervé
MaRDI profile type: Publication
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Wikidata QID: Q59288623
full work available at URL: s0012-7094-94-07502-9
OpenAlex ID: W1488032022
description: scientific article; zbMATH DE number 706706