Overview
- 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
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (4 chapters)
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Front Matter
Keywords
About this book
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 interestto all researchers in the field.
Reviews
“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)
Authors and Affiliations
About the authors
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.Bibliographic Information
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
DOI: https://doi.org/10.1007/978-3-030-29530-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-29529-5Published: 13 November 2019
eBook ISBN: 978-3-030-29530-1Published: 31 October 2019
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XI, 127
Number of Illustrations: 1 b/w illustrations, 2 illustrations in colour
Topics: Partial Differential Equations, Systems Theory, Control