Solution for the Geometric Elastostatic Inverse Problem by Means of Not Completely Overdetermined Boundary Data

The problem of detecting and localizing a cavity, a crack, or an inclusion in an elastic body by means of partially overdetermined data given on its outer boundary is considered. The input data can be obtained in a single static experiment. A new approach for solving this problem is proposed. The capabilities of the proposed approach are illustrated by the example of the problem for detecting a cavity in an elastic plate.