Uniqueness in Identification of the Support of a Source Term in an Elliptic Equation

We consider an inverse problem of identifying the support D of a source term in an elliptic equation −∆u(x) + q(x)χD(x)u(x) = 0, x ∈ Ω and u(x) = f(x), x ∈ ∂Ω. Here q is a given positive function and χD is the characteristic function of a subdomain D such that D ⊂ Ω. By using a Carleman estimate, we prove the global uniqueness in this inverse problem within convex hulls of polygons D’s.