Overview
- 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
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
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.
Authors and Affiliations
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