On the blowup of quantitative unique continuation estimates for waves and applications to stability estimates

Overview & Synopsis

In this paper we are interested in the blowup of a geometric constant C(δ) appearing in the optimal quantitative unique continuation property for wave operators. In a particular geometric context we prove an upper bound for C(δ) as δ goes to 0. Here δ > 0 denotes the distance to the maximal unique continuation domain. As applications we obtain stability estimates for the unique continuation property up to the maximal domain. Using our abstract framework [FO25] we also derive a stability estimate for a hyperbolic inverse problem. The proof is based on a global explicit Carleman estimate combined with the propagation techniques of [LL19].