Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary

The main result of the present paper consists in a quantitative estimate of unique continuation at the boundary for solutions to the wave equation. Such estimate is the sharp quantitative counterpart of the following strong unique continuation property: let u be a solution to the wave equation that satisfies an homogeneous Robin condition on a portion S of the boundary and the restriction of u|S on S is flat on a segment {0} × J with 0 \in S then u|S vanishes in a neighborhood of {0} × J.