EAN: 9783030159924

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Over the past 25 years Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory inverse problems or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities driven by applications to various questions of unique continuation.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 between Holmgren'sand 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.

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