Carleman Estimates for Second Order Parabolic Operators and Applications, a Unified Approach

  • Xiaoyu FuEmail author
  • Qi Lü
  • Xu Zhang
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


In this chapter, we establish three Carleman estimates with different weight functions for second order parabolic operators. The first one is Theorem 3.1, which is used to obtain controllability/observability results for parabolic equations in Sect. 3.2. The second one is Theorem 3.2, via which, we solve an inverse parabolic problem in Sect. 3.3. The third one is Theorem 3.3, and it yields the SUCP of parabolic equations in Sect. 3.4.


Carleman estimate Second order parabolic operator Null controllability Strong unique continuation Three cylinders inequality 


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© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of MathematicsSichuan UniversityChengduChina

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