Carleman Estimates for Second Order Partial Differential Operators and Applications
A Unified Approach
Authors: Fu, Xiaoyu, Lü, Qi, Zhang, Xu
Free Preview- Self-contained introduction to Carleman estimates for three typical second order partial differential equations
- All Carleman estimates are derived from a fundamental identity for a second order partial differential operator
- Of wide interest to researchers in the field
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- About this book
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This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.
- About the authors
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Xiaoyu Fu is Professor of Mathematics in the School of Mathematics, Sichuan University, Chengdu, China. Her main research interest is control theory of partial differential equations.
Qi Lü is a Professor in the School of Mathematics, Sichuan University, Chengdu, China. His main research interest is Mathematical Control Theory, including in particular control theory of deterministic and stochastic partial differential equations.
Xu Zhang is Cheung Kong Scholar Distinguished Professor in the School of Mathematics, Sichuan University, Chengdu, China. His main research interests include mathematical control theory and related partial differential equations and stochastic analysis. - Reviews
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“The book will be useful for specialists in the respective area of mathematical analysis as well as for specialists in the field of control theory.” (Vyacheslav I. Maksimov, zbMATH 1445.35006, 2020)
- Table of contents (4 chapters)
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Introduction
Pages 1-15
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Carleman Estimates for Second Order Elliptic Operators and Applications, a Unified Approach
Pages 17-57
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Carleman Estimates for Second Order Parabolic Operators and Applications, a Unified Approach
Pages 59-88
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Carleman Estimates for Second Order Hyperbolic Operators and Applications, a Unified Approach
Pages 89-127
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Table of contents (4 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Carleman Estimates for Second Order Partial Differential Operators and Applications
- Book Subtitle
- A Unified Approach
- Authors
-
- Xiaoyu Fu
- Qi Lü
- Xu Zhang
- Series Title
- SpringerBriefs in Mathematics
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-29530-1
- DOI
- 10.1007/978-3-030-29530-1
- Softcover ISBN
- 978-3-030-29529-5
- Series ISSN
- 2191-8198
- Edition Number
- 1
- Number of Pages
- XI, 127
- Number of Illustrations
- 1 b/w illustrations, 2 illustrations in colour
- Topics
