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In this paper the discrete eigenvalues of elliptic second order differentialoperators in $L^2(\mathbb{R}^n)$, $n \in \mathbb{N}$, with singular $\delta$-and $\delta'$-interactions are studied. We show the self-adjointness of theseoperators and derive equivalent formulations for the eigenvalue problemsinvolving boundary integral operators. These formulations are suitable for thenumerical computations of the discrete eigenvalues and the correspondingeigenfunctions by boundary element methods. We provide convergence results andshow numerical examples.

Boundary integral formulations of eigenvalue problems for elliptic  differential operators with singular interactions and their numerical  approximation by boundary element methods