Carleman Estimate for the Wave Equation on a Riemannian Manifold

In this chapter, we prove a Carleman estimate with a second large parameter for a second-order hyperbolic operator on a Riemannian manifold MM. Our Carleman estimate holds in the whole cylindrical domain Q=M×(0,T)Q=M×(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. © 2017, Springer Science and Business Media Deutschland GmbH. All rights reserved.