Carleman estimates and observability inequalities for parabolic   equations with interior degeneracy
  We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on controllability results through Carleman estimates for the associated adjoint problem. The novelty of the present paper is that the degeneracy is also in the interior of the control region, so that no previous result can be adapted to this situation. 
Genni Fragnelli, Dimitri Mugnai
math.AP math.OC