Carleman Inequalities

Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book''s first five chapters contain a thorough exposition of the most classical results, such as Calderón''s and Hörmander''s theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results betweenHolmgren''s and Hörmander''s uniqueness theorems, Wolff''s modification of Carleman''s method, conditional pseudo-convexity, and more.

With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.