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We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we 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, the problem is considered as one with an interior degeneracy and Neumann boundary conditions, so no previous result can be adapted to this situation. As a consequence, new observability inequalities are established.

Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions