Illinois Journal of Mathematics

Symmetry of a boundary integral operator and a characterization of a ball

Mikyoung Lim

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Abstract

If $\ohm$ is a ball in $\Real ^n$ $(n\geq 2)$, then the boundary integral operator of the double layer potential for the Laplacian is self-adjoint on $L^2({\partial}{\ohm})$. In this paper we prove that the ball is the only bounded Lipschitz domain on which the integral operator is self-adjoint.

Article information

Source
Illinois J. Math., Volume 45, Number 2 (2001), 537-543.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138354

Digital Object Identifier
doi:10.1215/ijm/1258138354

Mathematical Reviews number (MathSciNet)
MR1878617

Zentralblatt MATH identifier
1003.31001

Subjects
Primary: 31B10: Integral representations, integral operators, integral equations methods
Secondary: 31B15: Potentials and capacities, extremal length 47G10: Integral operators [See also 45P05]

Citation

Lim, Mikyoung. Symmetry of a boundary integral operator and a characterization of a ball. Illinois J. Math. 45 (2001), no. 2, 537--543. doi:10.1215/ijm/1258138354. https://projecteuclid.org/euclid.ijm/1258138354


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