Exterior Dirichlet boundary value problem of reduced wave equation (Q2706035)

The author investigates an interesting problem of non-homogeneous reduced wave equation or Helmholtz equation \((\triangle -\lambda ^2)u(x,\lambda)=f(x)\) in \(\Omega \) with \(u(x)=0\) on \(\partial \Omega \). The solution of the considered problem is represented using Newtonian single-layer and double-layer potentials with complex parameter \(\lambda \). The resolvent is extended analytically to the imaginary axis.