Carleman Estimates for Second Order Partial Differential Operators and Applications

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 continuati

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Xiaoyu Fu Qi Lü Xu Zhang

Carleman Estimates for Second Order Partial Differential Operators and Applications A Unified Approach 123

SpringerBriefs in Mathematics Series Editors Nicola Bellomo, Torino, Italy Michele Benzi, Pisa, Italy Palle Jorgensen, Iowa, USA Tatsien Li, Shanghai, China Roderick Melnik, Waterloo, Canada Otmar Scherzer, Linz, Austria Benjamin Steinberg, New York, USA Lothar Reichel, Kent, USA Yuri Tschinkel, New York, USA George Yin, Detroit, USA Ping Zhang, Kalamazoo, USA

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BCAM SpringerBriefs Editorial Board Enrique Zuazua Deusto Tech Universidad de Deusto Bilbao, Spain and Departamento de Matemáticas Universidad Autónoma de Madrid Cantoblanco, Madrid, Spain Irene Fonseca Center for Nonlinear Analysis Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, USA Juan J. Manfredi Department of Mathematics University of Pittsburgh Pittsburgh, USA Emmanuel Trélat Laboratoire Jacques-Louis Lions Institut Universitaire de France Université Pierre et Marie Curie CNRS, UMR, Paris Xu Zhang School of Mathematics Sichuan University Chengdu, China BCAM SpringerBriefs aims to publish contributions in the following disciplines: Applied Mathematics, Finance, Statistics and Computer Science. BCAM has appointed an Editorial Board, who evaluate and review proposals. Typical topics include: a timely report of state-of-the-art analytical techniques, bridge between new research results published in journal articles and a contextual literature review, a snapshot of a hot or emerging topic, a presentation of core concepts that students must understand in order to make independent contributions. Please submit your proposal to the Editorial Board or to Francesca Bonadei, Executive Editor Mathematics, Statistics, and Engineering: [email protected].

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Xiaoyu Fu Qi Lü Xu Zhang •



Carleman Estimates for Second Order Partial Differential Operators and Applications A Unified Approach

123

Xiaoyu Fu School of Mathematics Sichuan University Chengdu, China

Qi Lü School of Mathematics Sichuan University Chengdu, China

Xu Zhang School of Mathematics Sichuan University Chengdu, China

ISSN 2191-8198 ISSN 2191-8201 (electronic) SpringerBriefs in Mathematics ISBN 978-3-030-29529-5 ISBN 978-3-030-29530-1 (eBook) https://doi.org/10.1007/978-3-030-29530-1 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustra