Carleman inequalities : an introduction and more

• 作者： Lerner, Nicolas, author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Grundlehren der mathematischen wissenschaften, a series of comprehensive studies in mathematics ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Grundlehren der mathematischen wissenschaften, a series of comprehensive studies in mathematics,volume 353
• 主題： Inequalities (Mathematics) , Carleman theorem. , Operator Theory. , Partial Differential Equations.
• ISBN： 9783030159931 (electronic bk.) 、 9783030159924 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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 Calderon's and Hormander'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 Hormander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more. With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.
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