The domain derivative and two applications in inverse scattering theory

The author recalls the notion of the domain derivative of a functional. The existence and a characterization of the domain derivative of the far-field pattern for a scattering problem with Dirichlet boundary condition is proved. The second part uses this characterization for an efficient implementation of a Gauss-Newton method for solving the inverse obstacle scattering problem. The author deals with the sensitivity of the linearized obstacle problem.