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

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