Recovery of the support of a source term in an elliptic differential equation

The recovery of a source term by exterior measurements is a challenging problem that arises in several applications. In this paper this nonlinear and ill-posed problem is investigated in the case where the source term is assumed to be known but its support is not. Global uniqueness results are presented as well as iterative numerical methods. The numerical approach is based on representing the derivative of the corresponding operator with respect to the boundary of the support.