On the Characterization of the Fr´echet Derivative with Respect to a Lipschitz Domain of the Acoustic Scattered Field

In this paper, we consider the Fr´echet differentiability with respect to a given domain of the solution of direct acoustic scattering problems with sound-soft, sound-hard, or lossy boundary conditions. We propose a new proof for characterizing the derivative of the acoustic scattered field as the solution of a particular direct scattering problem. This proof assumes that the boundary of the scatterer is only Lipschitzian and therefore extends this well-known characterization to obstacles with rough surfaces. Our result can be of practical interest because the characterization of the derivative of the acoustic scattered field has a great potential for the solution of inverse acoustic scattering problems by Newton-type methods. Q