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Summer 2008 Spectral properties of the layer potentials on Lipschitz domains
TongKeun Chang, Kijung Lee
Illinois J. Math. 52(2): 463-472 (Summer 2008). DOI: 10.1215/ijm/1248355344

Abstract

We study the invertibility of the operator $ \beta I - K^*$ in $H^{-\alpha} (\partial\Omega),\ 0\leq\alpha\leq1$ for $\beta\in \mathbf{C} \setminus(-\frac12 , \frac12]$ where $K^*$ is a adjoint operator of the double layer potential $K$ related to the Laplace equation and $\Omega$ is a bounded Lipschitz domain in $\mathbf{R}^n$. Consequently, the spectrum on the real line lies in $(-\frac12 , \frac12]$.

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TongKeun Chang. Kijung Lee. "Spectral properties of the layer potentials on Lipschitz domains." Illinois J. Math. 52 (2) 463 - 472, Summer 2008. https://doi.org/10.1215/ijm/1248355344

Information

Published: Summer 2008
First available in Project Euclid: 23 July 2009

zbMATH: 1205.31001
MathSciNet: MR2524646
Digital Object Identifier: 10.1215/ijm/1248355344

Subjects:
Primary: 31B10
Secondary: 45210

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 2 • Summer 2008
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