On C. Neumann's Method for Second-Order Elliptic Systems in Domains with Non-smooth Boundaries

AbstractIn this paper we investigate the convergence of Carl Neumann's method for the solution of Dirichlet or Neumann boundary values for second-order elliptic problems in domains with non-smooth boundaries. We prove that 12I+K, where K is the double-layer potential, is a contraction in H1/2(Γ) when an energy norm is used that is induced by the inverse of the single-layer potential