Carleman estimates and their applications to inverse problems

We consider Carleman type estimates for general second order partial differential operators with real-valued coefficients. We include boundary terms. We give a derivation of these estimates, examples for elliptic and hyperbolic equations. As applications we consider uniqueness and stability in the Cauchy problem (in particular increased stability for the Helmholtz equation) and identification of coefficients and source terms of hyperbolic equations from the lateral Cauchy data.