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

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

Abstract

In this chapter, we establish two Carleman estimates (with different weight functions) for second order elliptic operators, i.e. Theorems 2.1 and 2.2. By means of the first one, we derive an interpolation inequality for elliptic equations, via which an observability estimate for sums of eigenfunctions of elliptic operators and a stabilization result for locally damped hyperbolic equations are proved. Based on the second one, we show a strong unique continuation property and a three-ball inequality for elliptic equations.

Keywords

Carleman estimate Second order elliptic operator Observability estimate Strong unique continuation Three-ball inequality 

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Copyright information

© 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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