Inverse source problem in an anisotropic medium by boundary measurements

In this paper, we consider an inverse source problem for an anisotropic elliptic equation, from boundary measurements. A uniqueness result is established and a local Lipshitz stability, for a linear combination of monopolar and dipolar sources, is discussed. Assuming the number of dipoles bounded by a given integer M, we propose an algebraic algorithm which allows us to estimate the number, the locations and the moments of dipoles. Using special functions, we propose a global Lipschitz stability estimate for dipolar sources.