Carleman Inequalities

An Introduction and More

  • Nicolas Lerner

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 353)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Nicolas Lerner
    Pages 1-25
  3. Nicolas Lerner
    Pages 27-46
  4. Nicolas Lerner
    Pages 69-92
  5. Nicolas Lerner
    Pages 93-136
  6. Nicolas Lerner
    Pages 137-193
  7. Nicolas Lerner
    Pages 195-236
  8. Nicolas Lerner
    Pages 415-442
  9. Back Matter
    Pages 443-557

About this book


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'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.


Carleman inequalities Carleman estimates Unique Continuation Strong Unique Continuation Pseudo-convexity Principal Normality Counterexamples to Uniqueness of the Cauchy Problem Operators with partially analytic coefficients Strichartz estimates Conditional pseudo-convexity

Authors and affiliations

  • Nicolas Lerner
    • 1
  1. 1.Institut de Mathématiques de JussieuSorbonne UniversitéParisFrance

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-15992-4
  • Online ISBN 978-3-030-15993-1
  • Series Print ISSN 0072-7830
  • Series Online ISSN 2196-9701
  • Buy this book on publisher's site