On a boundary value problem in the theory of linear water waves

A body Ω floating in a fluid is subjected to small periodic displacement. Under idealized conditions the resulting wave pattern can be described by a linear boundary value problem for the Laplacian in an unbounded domain with a non-coercive boundary condition on part of the boundary. Nevertheless uniqueness can be shown if Ω is confined to certain subsets of the fluid which can be described explicitly. This extends a result of V. G. Maz'ja saying that uniqueness holds provided that the exterior normal for ?Ω avoids certain directions.