Uniqueness of Solutions to the Helically Reduced Wave Equation with Sommerfeld Boundary Conditions

We consider the helical reduction of the wave equation with an arbitrary source on (n+1)-dimensional Minkowski space, n ≥ 2. The reduced equation is of mixed elliptic-hyperbolic type on Rn. We obtain a uniqueness theorem for solutions on a domain consisting of an n-dimensional ball B centered on the reduction of the axis of helical symmetry and satisfying ingoing or outgoing Sommerfeld conditions on ∂B ≈ Sn−1. Non-linear generalizations of such boundary value problems (with n = 3) arise in the intermediate phase of binary inspiral in general relativity.