Stability of the unique continuation for the wave operator via Tataru inequality and applications

الأصل · EN

In this paper we study the stability of the unique continuation in the case of the wave equation with variable coefficients independent of time. We prove a logarithmic estimate in a arbitrary domain of Rⁿ⁺¹, where all the parameters are calculated explicitly in terms of the C¹-norm of the coefficients and on the other geometric properties of the problem. We use the Carleman-type estimate proved by Tataru in 1995 and an iteration for locals stability. We apply the result to the case of a wave equation with data on a cylinder an we get a stable estimate for any positive time, also after the first conjugate point for the geodesics of the metric related to the variable coefficients.