Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains.

It is well known that, with a particular choice of norm, the classical double-layer potential operator $D$ has essential norm $ 0$, examples of Lipschitz polyhedra for which the essential norm is $\geq C$ and for which $\lambda I+D$ is not a compact perturbation of a coercive operator for any real or complex $\lambda$ with $|\lambda|\leq C$. Finally, we resolve negatively a related open question in the convergence theory for collocation methods.