Carleman estimates and observability inequalities for parabolic equations with interior degeneracy

Abstract

We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on Carleman estimates for the associated adjoint problem. The novelty of interior degeneracy does not let us adapt previous Carleman estimates to our situation. As an application, observability inequalities are established.

Keywords

• degenerate equation
• interior degeneracy
• carleman estimates
• observability inequalities