The paper, as the author states, provides a partial answer to the problem of finding the shape of a hole from outer boundary measurements.
Crosta, G. (1996). Mathematical Review: MR1343271 Nakamura, Gen Identification of the shape of a hole inside an elastic medium. Geometry and its applications (Yokohama, 1991), 195–200, World Sci. Publ., River Edge, NJ, 1993. MATHEMATICAL REVIEWS, 96e, 73023-73023.