Recovery of an unknown support of a source term in an elliptic equation

Abstract

In this paper, we consider the inverse problem of determining the shape and location of inhomogeneity D in an elliptic equation with a Neumann boundary condition on ∂Ω where and χD is the characteristic function of a subdomain D. We discuss the global uniqueness in determining D by a single measurement of Dirichlet data u on ∂Ω and prove uniqueness results with extra information on domains D.