Method of interior boundaries for the impedance problem in scattering theory. (Q1855970)

The author proposes yet another scheme for obtaining a solution \(W\) to the third boundary value problem for Helmholtz' equation in an exterior domain \(D := \mathbb R^m \setminus \overline{{\bigcup_n}\Omega_n}\) , \(\Omega_n\) (bounded domains) \(\subset \mathbb R^m\) : Extend \(W\) by solutions \(u_n\) of Helmholtz' equation in \(\Omega_n \setminus B_n,\) \(B_n := B(x_n,\rho)\) subject to the boundary conditions \(u_n = W\) on \(\partial \Omega_n\) and \(\frac{\partial}{\partial n} u_n - i \cdot u_n = 0\) on \(\partial B_n\). The extended solution may then be found by solving an integral equation.