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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 interestto all researchers in the field.
List of contents
1 Introduction.- 2 Carleman estimates for second order elliptic operators and applications.- 3 Carleman estimates for second order parabolic operators and applications.- 4 Carleman estimates for second order hyperbolic operators and applications.
About the author
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.
Summary
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.
Report
"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)
