Convergence of the Neumann series for a Helmholtz-type equation

Abstract

We pursue a constructive solution to the Robin problem of a Helmholtz-type equation in the form of a single layer potential. This representation method leads to a boundary integral equation. We study the problem on a bounded planar domain of class C2. We prove the convergence of the Neumann series of iterations of the layer potential operators to the solution of the boundary integral equation. This study is inspired by several recent papers which cover the iteration techniques. In [7], [8], [9], D. Medkova obtained results regarding the successive approximation method for Neumann, Robin and transmission problems.