On an integral equation approach for the exterior Robin problem for the Helmholtz equation (Q1098997)

The boundary integral equation representation of the exterior Robin problem for the Helmholtz equation involves a non-compact integral operator. Previously a suitable regularization of the non-compact operator has been introduced in order to make the Fredholm alternative available. Here the author presents a direct proof of existence and uniqueness of the required solutions in the settings \(C^{1,\lambda}(S)\) and \(C^{0,\lambda}(S)\), where S is a closed smooth bounded surface, which does not rely on a regularization process being introduced.