Graduate School of Mathematical Sciences Komaba, Tokyo, Japan Recovery of a Support of a Source Term in an Elliptic Equation

This paper deals with an inverse problem of determining the shape and location of inhomogeneity D in an elliptic equation with a Neumann boundary condition ∂u ∂ν = g on ∂Ω −∆u(x) + pχD(x)u(x) = 0, x ∈ Ω, where D ⊂ Ω and χD is the characteristic function of a subdomain D. We prove the global uniqueness in this inverse problem by a single measurement of Dirichlet data u on ∂Ω.