Multi-parameter analysis of the obstacle scattering problem

We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Delta u + k (2) u = 0. We show that the solution u and its far field pattern u (infinity) depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.