On the characterization of the Frechet derivative with respect to a Lipschitz domain of the acoustic scattered field

In this paper, we consider the Frechet differentiability with respect to a given domain of the solution of direct acoustic scattering problems with so und-soft, sound-hard, or lossy boundary conditions. We propose a new proof for characterizing the derivative of the acoustic scattered field as the so lution of a particular direct scattering problem. This proof assumes that t he boundary of the scatterer is only Lipschitzian and therefore extends thi s 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. (C) 1999 Acade mic Press.