Thin sets and boundary behavior of solutions of the Helmholtz equation (Q1282071)

The authors study the boundary behaviour of solutions to the Helmholtz equation. They define a notion of a thin set at the boundary. Then they prove that for each positive solution of the Helmholtz equation \(n\), there is a thin set such that \(n/v\) has a limit at almost every point of the sphere (identified as the Martin boundary), if boundary points are approached with respect to the Martin topology outside this thin set. Here \(v\) denotes the solution that is represented by the Lebesgue surface measure on the sphere.