Remarks on the inverse scattering problem for low frequency acoustic waves

In a recent series of papers (2, 3, 4) the author has investigated the low frequency inverse scattering problem for 'hard' and 'soft' infinite cylinders and 'soft' obstacles in space. It is the purpose of this paper to complete the story and consider the inverse scattering problem in space where the obstacle is 'hard', i.e. the boundary condition is of Neumann type. A basic result of the analysis to date is that the low frequency inverse scattering problem can be stabilized. In the case of domains in the plane this is accomplished by transmitting two plane waves from different directions, where the second plane wave is used to determine the transfinite diameter of the obstacle.