Spectral properties of the layer potentials on Lipschitz domains
type: Item
instance of: scholarly article
title: Spectral properties of the layer potentials on Lipschitz domains
zbMATH Open document ID: 1205.31001
author: Kijung Lee
author: Tongkeun Chang
published in: Illinois Journal of Mathematics
publication date: 2009-10-15T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1248355344
review text: Let \(K\) be the double layer potential related to the Laplace equation on a bounded Lipschitz domain \(\Omega\) in \({\mathbb R}^n\), \(n\geq 2\), and let \(K^*\) be the adjoint of \(K\). The authors study some spectral properties of \(K^*\). In particular, they show that when \(\Omega\) is a locally convex bounded Lipschitz domain, then \(\beta I-K^*\) is invertible in \(H^{-\alpha}(\partial \Omega)\), \(\alpha\in [0, 1]\), for all complex numbers \(\beta\) with \(|\beta|>\frac12\), and that when \(\Omega\) is an arbitrary bounded Lipschtitz domain, then \(\beta I-K^*\) is invertible in \(H^{-1/2}(\partial \Omega)\) for all \(\beta\in {\mathbb C}\setminus (-\frac12, \frac12]\).
reviewed by: Renming Song
Mathematics Subject Classification ID: 31B10
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 5615648
zbMATH Keywords: single layer potential
zbMATH Keywords: double layer potential
zbMATH Keywords: Lipschitz domain
zbMATH Keywords: resolvent
zbMATH Keywords: spectrum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5615648