Singular parabolic equations with interior degeneracy and non smooth coefficients: The Neumann case

We establish Hardy - Poincare and Carleman estimates for non-smooth degenerate/singular parabolic operators in divergence form with Neumann boundary conditions. The degeneracy and the singularity occur both in the interior of the spatial domain. We apply these inequalities to deduce well-posedness and null controllability for the associated evolution problem.