Dang Dinh Ang

Abstarct
The author makes a survey of some recent developments on the problem of detecting cavities inside a solid body from measurements performed on its surface. Three groups of problems are considered. The first group takes its origin from the problem of detecting cracks inside a solid by the electric method and in its simplest form, it is equivalent to the problem of identifying the domain of the Laplace equation. The second group is related to the problem of detecting cracks in the interior of an elastic body. The third group is related to the problem of detecting mass inhomogeneities inside the Earth from gravity anomalies or gravity gradients measured on the surface. All of these problems are nonlinear. They are approximated by various methods: the method of finite dimensional approximations and the method of linearization.