Single logarithmic conditional stability in determining unknown boundaries

We prove a conditional stability estimate of log-type for determining unknown boundaries from a single Cauchy data taken on an accessible sub-boundary. Our approach relies on new interior and boundary estimates for elliptic equations which are derived from the Carleman estimate. Stability results for target identification of an acoustic sound-soft scatterer from one or several far-field patterns are also obtained. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.