Frechet differentiability of boundary integral operators in inverse acoustic scattering

Using integral equation methods to solve the time-harmonic acoustic scattering problem with Dirichlet boundary conditions, it is possible to reduce the solution of the scattering problem to the solution of a boundary integral equation of the second kind. We show the Frechet differentiability of the boundary integral operators which occur. We then use this to prove the Frechet differentiability of the scattered field with respect to the boundary. Finally we characterize the Frechet derivative of the scattered field by a boundary value problem with Dirichlet conditions, in an analogous way to that used by Firsch.