Details

Carleman Inequalities


Carleman Inequalities

An Introduction and More
Grundlehren der mathematischen Wissenschaften, Band 353

von: Nicolas Lerner

128,39 €

Verlag: Springer
Format: PDF
Veröffentl.: 18.05.2019
ISBN/EAN: 9783030159931
Sprache: englisch

Dieses eBook enthält ein Wasserzeichen.

Beschreibungen

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.<div><br></div><div>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 betweenHolmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more.</div><div><br></div><div>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. </div>
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.
Nicolas Lerner is professor at Sorbonne Université (formerly Université Paris VI). He has written several articles on Carleman estimates and a book on pseudo-differential operators. He was an invited section speaker at the 2002 ICM in Beijing.
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.<div><br></div><div>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 betweenHolmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more.</div><div><br></div><div>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.</div>
Provides an accessible introduction to Carleman estimates Includes recent results, examples, and applications Written by an expert in the field

Diese Produkte könnten Sie auch interessieren:

Classical Fourier Analysis
Classical Fourier Analysis
von: Loukas Grafakos
PDF ebook
50,24 €
Nonsmooth Dynamics of Contacting Thermoelastic Bodies
Nonsmooth Dynamics of Contacting Thermoelastic Bodies
von: Jan Awrejcewicz, Yuriy Pyr'yev
PDF ebook
106,99 €
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
von: Kenneth Meyer, Glen Hall, Dan Offin
PDF ebook
106,99 €