Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries

In this paper we obtain quantitative estimates of strong unique continuation for solutions to parabolic equations. We apply these results to prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain Ω Ω in R n Rⁿ , from the knowledge of overdetermined boundary data for parabolic boundary value problems.