Authors:
- Provides an accessible introduction to Carleman estimates
- Includes recent results, examples, and applications
- Written by an expert in the field
Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 353)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- 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
- partial differential equations
Authors and Affiliations
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Institut de Mathématiques de Jussieu, Sorbonne Université, Paris, France
Nicolas Lerner
About the author
Bibliographic Information
Book Title: Carleman Inequalities
Book Subtitle: An Introduction and More
Authors: Nicolas Lerner
Series Title: Grundlehren der mathematischen Wissenschaften
DOI: https://doi.org/10.1007/978-3-030-15993-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-15992-4Published: 29 May 2019
eBook ISBN: 978-3-030-15993-1Published: 18 May 2019
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 1
Number of Pages: XXVII, 557
Number of Illustrations: 97 b/w illustrations, 10 illustrations in colour