  In this work, we shall study the nonlinear inverse problems of recovering the
Robin coefficients in elliptic and parabolic systems of second order, and
establish their local Lipschitz stabilities. Some local Lipschitz stability was
derived for an elliptic inverse Robin problem. We shall first restructure the
arguments in \cite{chou04} for the local Lipschitz stability so that the
stability follows from three basic conditions for the elliptic inverse Robin
problem. The new arguments are then generalized to help establish a novel local
Lipschitz stability for parabolic inverse Robin problems.
