Carleman Estimate for the Wave Equation on a Riemannian Manifold

Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter, we prove a Carleman estimate with a second large parameter for a second-order hyperbolic operator on a Riemannian manifold \(\mathrm {M}\). Our Carleman estimate holds in the whole cylindrical domain \(Q=\mathrm {M}\times (0,T)\) independently of the level set generated by a weight function. The proof is direct, relying on the calculus of tensor fields on a Riemannian manifold.

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© Springer Japan KK 2017

Authors and Affiliations

  1. 1.Department of MathematicsENIT—LAMSIN, University of Tunis El ManarTunisTunisia
  2. 2.Department of Mathematical SciencesThe University of TokyoTokyoJapan
  3. 3.Research Center of Nonlinear Problems of Mathematical PhysicsPeoples’ Friendship University of RussiaMoscowRussia

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