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. Copyright © 1990 John Wiley & Sons, Ltd