On C. Neumann's method for second-order elliptic systems in domains with non-smooth boundaries

Abstract

In 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 1/2I + K, where K is the double-layer potential, is a contraction in H1/2(L) when an energy norm is used that is induced by the inverse of the single-layer potential. © 2001 Academic Press.