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Grundlehren der mathematischen Wissenschaften

Carleman Inequalities

An Introduction and More

Authors: Lerner, Nicolas

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  • Provides an accessible introduction to Carleman estimates
  • Includes recent results, examples, and applications
  • Written by an expert in the field
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  • ISBN 978-3-030-15993-1
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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.

About the authors

Nicolas Lerner is professor at Sorbonne Université (formerly Université Paris VI). He has written several articles on Carleman estimates and a book on pseudo-differential operators. He was an invited section speaker at the 2002 ICM in Beijing.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook 96,29 €
price for Spain (gross)
  • ISBN 978-3-030-15993-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-030-15992-4
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Carleman Inequalities
Book Subtitle
An Introduction and More
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
353
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-15993-1
DOI
10.1007/978-3-030-15993-1
Hardcover ISBN
978-3-030-15992-4
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XXVII, 557
Number of Illustrations
97 b/w illustrations, 10 illustrations in colour
Topics

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