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.
Citation
Mikyoung Lim. "Symmetry of a boundary integral operator and a characterization of a ball." Illinois J. Math. 45 (2) 537 - 543, Summer 2001. https://doi.org/10.1215/ijm/1258138354
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