Stability of the unique continuation for the wave operator via Tataru inequality: the local case

Abstract

In 1995, Tataru proved a Carleman-type estimate for linear operators with partially analytic coefficients that is generally used to prove the unique continuation of those operators. In this paper, we use this inequality to study the stability of the unique continuation in the case of the wave equation with coefficients independent of time. We prove a logarithmic estimate in a ball whose radius has an explicit dependence on the C1-norm of the coefficients and on the other geometric properties of the operator.