  The approach to Lipschitz stability for uniformly parabolic equations
introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates,
seems hard to apply to the case of Grushin-type operators studied in this
paper. Indeed, such estimates are still missing for parabolic operators
degenerating in the interior of the space domain. Nevertheless, we are able to
prove Lipschitz stability results for inverse coefficient problems for such
operators, with locally distributed measurements in arbitrary space dimension.
For this purpose, we follow a strategy that combines Fourier decomposition and
Carleman inequalities for certain heat equations with nonsmooth coefficients
(solved by the Fourier modes).
