Spectral boundary value problems for the Helmholtz equation with spectral parameter in boundary conditions on a non-smooth surface

The spectral properties of four problems for the Helmholtz equation with spectral parameter in boundary or transmission conditions on a closed Lipschitz surface $S$ are studied. These problems are related to the classical integral operators of potential type on $S$ for the Helmholtz equation. They have been studied before in the case when $S$ is infinitely smooth. It is shown that the most important properties of eigenvalues and root functions hold also for Lipschitz surfaces $S$. The machinery of potential theory in Lipschitz domains and of spectral theory is used in the proofs.