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We consider a parabolic problem with degeneracy in the interior of\udthe spatial domain, and we focus on observability results through\udCarleman estimates for the associated adjoint problem. The novelties\udof the present paper are two. First, the coefficient of the leading operator only\udbelongs to a Sobolev space. Second, the degeneracy point is allowed to lie\udeven in the interior of the control region, so that no previous\udresult can be adapted to this situation; however, different\udcases can be handled, and new controllability results are\udestablished as a consequence

Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Non Smooth Parabolic Equations