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

About this Title

Genni Fragnelli and Dimitri Mugnai

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 242, Number 1146
ISBNs: 978-1-4704-1954-7 (print); 978-1-4704-2946-1 (online)
Published electronically: February 29, 2016

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Table of Contents


  • Chapter 1. Introduction
  • Chapter 2. Mathematical tools and preliminary results
  • Chapter 3. Carleman estimate for non degenerate parabolic problems with non smooth coefficient
  • Chapter 4. Carleman estimate for degenerate non smooth parabolic problems
  • Chapter 5. Observability inequalities and application to null controllability
  • Chapter 6. Linear and Semilinear Extensions
  • Chapter 7. Final Comments
  • Appendix A. Rigorous derivation of Lemma 3.5


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

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