Double layer potentials on three-dimensional wedges and pseudodifferential operators on Lie groupoids
type: Item
instance of: scholarly article
title: Double layer potentials on three-dimensional wedges and pseudodifferential operators on Lie groupoids
zbMATH Open document ID: 1437.35152
author: Yu Qiao
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-05-31T00:00:00Z
review text: The paper aims to examine the analytic properties of \(\frac{1}{2}\pm K\) operator on a three-dimensional wedge \(\mathcal{W}\), where \(K\) denotes the so-called direct value of the double-layer potential, associated to the Laplacian, calculated over the wedge \(\mathcal{W}\). It is shown that \(\frac{1}{2}\pm K\) are isomorphisms between suitable weighted Sobolev spaces, which implies a solvability result in weighted Sobolev spaces for the Dirichlet problem on \(\mathcal{W}\). Besides, the connection between the operator \(K\) with a pseudo-differential operator algebra on some Lie groupoid is investigated. The result can be used to prove the Fredholmness of \(\frac{1}{2}\pm K_\Omega\), where \(\Omega\) is ``a domain with edge singularities'' and \(K_\Omega\) is the direct value of the double layer potential operator associated to the Laplacian, calculated over \(\Omega\).
reviewed by: D. Kapanadze
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 31B20
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 22A22
zbMATH DE Number: 6877134
zbMATH Keywords: method of layer potentials
zbMATH Keywords: double layer potential operator
zbMATH Keywords: convolution integral operator
zbMATH Keywords: groupoid \({C}^*\)-algebra
zbMATH Keywords: weighted Sobolev space
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.01.077
OpenAlex ID: W2793566386
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Double layer potentials on three-dimensional wedges and pseudodifferential operators on Lie groupoids (DOI)
DOI: 10.1016/J.JMAA.2018.01.077