IUMJ

Title: Cracks with impedance; stable determination from boundary data

Authors: Giovanni Alessandrini and Eva Sincich

Issue: Volume 62 (2013), Issue 3, 947-989

Abstract:

We discuss the inverse problem of determining the possible presence of an $(n-1)$-dimensional crack $\Sigma$ in an $n$-dimensional body $\Omega$ with $n\geqslant3$ 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 N-D map are available.