Quantitative estimates of strong unique continuation for wave equations

The main results of the present paper consist in some quantitative estimates for solutions to the wave equation u_{tt}−div (A(x)∇u) = 0. Such estimates imply the following strong unique continuation properties: (a) if u is a solution to the the wave equation and u is flat on a segment {0}xJ on the t axis, then u vanishes in a neigh- borhood of {0}xJ. (b) Let u be a solution of the above wave equation in Q× J that vanishes on a a portion Z × J where Z is a portion of the boundary of Q and u is flat on a segment {0} × J, 0 ∈ Z, then u vanishes in a neighborhood of {0} × J.