  We consider a parabolic problem with degeneracy in the interior of the
spatial domain and Neumann boundary conditions. In particular, we will focus on
the well-posedness of the problem and on Carleman estimates for the associated
adjoint problem. The novelty of the present paper is that for the first time it
is considered a problem with an interior degeneracy and Neumann boundary
conditions so that no previous result can be adapted to this situation. As a
consequence new observability inequalities are established.
