A limiting absorption principle for scattering problems with unbounded obstacles

A generalized mode matching method that applies to a wide class of scattering problems is developed in the time harmonic two-dimensional Helmholtz case. This method leads by variational means to an integro-differential formulation whose unknown is the trace of the field on an unbounded one-dimensional interface. The well-posedness is proved after a careful study of the rather original functional framework. Owing to a fundamental density result-based upon some properties of a singular integral operator similar to the Hilbert transform-the limiting absorption principle related to this original formulation is established. Finally, two other situations are emphasized.