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