  This is a survey, which is a continuation of the previous survey of the
author about applications of Carleman estimates to Inverse Problems, J. Inverse
and Ill-Posed Problems, 21, 477-560, 2013. It is shown here that Tikhonov
functionals for some ill-posed Cauchy problems for linear PDEs can be generated
by unbounded linear operators of those PDEs. These are those operators for
which Carleman estimates are valid, e.g. elliptic, parabolic and hyperbolic
operators of the second order. Convergence rates of minimizers are established
using Carleman estimates. Generalizations to nonlinear inverse problems, such
as problems of reconstructions of obstacles and coefficient inverse problems
are discussed as well.
