Stability result for elliptic inverse periodic coefficient problem by   partial Dirichlet-to-Neumann map
  We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the potential with respect to the partial Dirichlet-to-Neumann map, where the Neumann data is taken on slightly more than half of the boundary of the domain. 
Mourad Choulli, Yavar Kian, Eric Soccorsi
math.AP