Inverse crack problem and probe method

A problem of extracting information about the location and shape of unknown cracks in a background medium from the Dirichlet-to-Neumann map is considered. An application of a new formulation of the probe method introduced by the author to the problem is given. The method is based on: the blowup property of sequences of special solutions of the governing equation for the background medium which are related to a singular solution of the equation; an explicit lower bound of an L2-norm of the gradient of the so-called reflected solution. AMS: 35R3