Continuous Frechet differentiability with respect to a Lipschitz domain and a stability estimate for direct acoustic scattering problems

We consider direct acoustic scattering problems with either a sound-soft or sound-hard obstacle, or lossy boundary conditions, and establish continuou s Frechet differentiability with respect to the shape of the scatterer of t he scattered field and its corresponding farfield pattern. Our proof is bas ed on the implicit function theorem, and assumes that the boundary of the s catterer as well as the deformation are only Lipschitz continuous. From con tinuous Frechet differentiability, we deduce a stability estimate governing the variation of the far-field pattern with respect to the shape of the sc atterer. We illustrate this estimate with numerical results obtained for a two-dimensional high-frequency acoustic scattering problem.