A proof for the Burton and Miller integral equation approach for the Helmholtz equation (Q1080054)

A function f belongs to the space \(C^{\ell,\lambda}(S)\) (S a closed bounded surface in \(R^ 3)\) if f is \(\ell\)-times continuous differentiable on S and if the \(\ell th\) order derivatives are Hölder continuous with exponent \(\lambda\). The author uses these spaces in order to give a rigorous proof of the existence and uniqueness theorem of the \textit{A. I. Burton} and \textit{G. F. Miller} integral equation formulation for Helmholtz's equation of the exterior Neumann problem [Proc. R. Soc. Lond. Ser. A 323, 201-210 (1971; Zbl 0235.65080)].