Cracks with impedance, stable determination from boundary data

We discuss the inverse problem of determining the possible presence of an $(n-1)$-dimensional crack $\Sigma$ in an $n$-dimensional body $\Omega$ with $n\ge 3$ when the so-called Dirichlet-to-Neumann map is given on the boundary of $\Omega$. In combination with quantitative unique continuation techniques, an optimal single-logarithm stability estimate is proven by using the singular solutions method. Our arguments also apply when the Neumann-to-Dirichlet map or the local versions of the D-N and the N-D map are available.