Carleman Inequalities : An Introduction and More. 1st ed. 2019

種類:

電子ブック

責任表示:

by Nicolas Lerner

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Lerner, Nicolas.
• SpringerLink (Online service)

シリーズ名:

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 353

ISBN:

9783030159931 [3030159930]    

注記:

1 Prolegomena -- 2 A Toolbox for Carleman Inequalities -- 3 Operators with Simple Characteristics: Calderon's Theorems -- 4 Pseudo-convexity: Hormander's Theorems -- 5 Complex Coefficients and Principal Normality -- 6 On the Edge of Pseudo-convexity -- 7 Operators with Partially Analytic Coefficients -- 8 Strong Unique Continuation Properties for Elliptic Operators -- 9 Carleman Estimates via Brenner's Theorem and Strichartz Estimates -- 10 Elliptic Operators with Jumps; Conditional Pseudo-convexity -- 11 Perspectives and Developments -- A Elements of Fourier Analysis -- B Miscellanea -- References -- Index.
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 theor

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