Illinois Journal of Mathematics

Spectral properties of the layer potentials on Lipschitz domains

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 $(-\frac12 , \frac12]$.

Article information

Source
Illinois J. Math., Volume 52, Number 2 (2008), 463-472.

Dates
First available in Project Euclid: 23 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1248355344

Digital Object Identifier
doi:10.1215/ijm/1248355344

Mathematical Reviews number (MathSciNet)
MR2524646

Zentralblatt MATH identifier
1205.31001

Subjects
Primary: 31B10: Integral representations, integral operators, integral equations methods
Secondary: 45210

Citation

Chang, TongKeun; Lee, Kijung. Spectral properties of the layer potentials on Lipschitz domains. Illinois J. Math. 52 (2008), no. 2, 463--472. doi:10.1215/ijm/1248355344. https://projecteuclid.org/euclid.ijm/1248355344

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