Introduction

Abstract

In 1939, T. Carleman introduced some weighted estimates to achieve uniqueness properties for the Cauchy problem of an elliptic operator in two dimensions. Estimates of this type now bear his name. In the late 50s A.-P. Calderón and L. Hörmander further developed Carleman’s method. To this day, the method based on Carleman estimates remains essential to prove unique continuation properties. In more recent years, the field of applications of Carleman estimates has gone beyond the original domain; they are also used in the study of stabilization and controllability properties of partial differential equations, two applications we shall consider in this book. Inverse problems are also a field of applications for Carleman estimate; we shall however not touch upon that subject.