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

2015/09/02 by Boutaayamou, Idriss, Fragnelli, Genni, Maniar, Lahcen
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.00863

Abstract

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

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