000890534 000__ 05977cam\a2200517Ii\4500
000890534 001__ 890534
000890534 005__ 20230306150109.0
000890534 006__ m\\\\\o\\d\\\\\\\\
000890534 007__ cr\cn\nnnunnun
000890534 008__ 190521s2019\\\\sz\\\\\\ob\\\\001\0\eng\d
000890534 019__ $$a1105173845
000890534 020__ $$a9783030159931$$q(electronic book)
000890534 020__ $$a3030159930$$q(electronic book)
000890534 020__ $$z9783030159924
000890534 0247_ $$a10.1007/978-3-030-15
000890534 035__ $$aSP(OCoLC)on1101966661
000890534 035__ $$aSP(OCoLC)1101966661$$z(OCoLC)1105173845
000890534 040__ $$aN$T$$beng$$erda$$epn$$cN$T$$dN$T$$dEBLCP$$dGW5XE$$dOCLCF$$dLQU$$dUKMGB
000890534 049__ $$aISEA
000890534 050_4 $$aQA295
000890534 08204 $$a515/.26$$223
000890534 1001_ $$aLerner, Nicolas,$$d1953-$$eauthor.
000890534 24510 $$aCarleman inequalities :$$ban introduction and more /$$cNicolas Lerner.
000890534 264_1 $$aCham :$$bSpringer,$$c[2019]
000890534 264_4 $$c©2019
000890534 300__ $$a1 online resource.
000890534 336__ $$atext$$btxt$$2rdacontent
000890534 337__ $$acomputer$$bc$$2rdamedia
000890534 338__ $$aonline resource$$bcr$$2rdacarrier
000890534 4901_ $$aGrundlehren der mathematischen Wissenschaften ;$$vvolume 353
000890534 504__ $$aIncludes bibliographical references and index.
000890534 5050_ $$aIntro; Preface; Acknowledgements; Contents; 1 Prolegomena; 1.1 Preliminaries; 1.2 Hyperbolicity, the Energy Method and Well-Posedness; 1.3 The Lax-Mizohata Theorems; 1.3.1 Strictly Hyperbolic Operators; 1.3.2 Ill-Posedness Examples; 1.4 Holmgren's Uniqueness Theorems; 1.5 Carleman's Method Displayed on a Simple Example; 1.5.1 The overline Equation; 1.5.2 The Laplace Equation; 2 A Toolbox for Carleman Inequalities; 2.1 Weighted Inequalities; 2.2 Conjugation; 2.3 Sobolev Spaces with Parameter; 2.4 The Symbol of the Conjugate; 2.5 Choice of the Weight
000890534 5058_ $$a3 Operators with Simple Characteristics: Calderón's Theorems3.1 Introduction; 3.2 Inequalities for Symbols; 3.3 A Carleman Inequality; 3.4 Examples; 3.4.1 Second-Order Real Elliptic Operators; 3.4.2 Strictly Hyperbolic Operators; 3.4.3 Products; 3.4.4 Generalizations of Calderón's Theorems; 3.5 Cutting the Regularity Requirements; 4 Pseudo-convexity: Hörmander's Theorems; 4.1 Introduction; 4.2 Inequalities for Symbols; 4.3 Pseudo-convexity; 4.3.1 Carleman Inequality, Definition; 4.3.2 Invariance Properties of Strong Pseudo-convexity; 4.3.3 Unique Continuation; 4.4 Examples
000890534 5058_ $$a4.4.1 Pseudoconvexity for Real Second-Order Operators4.4.2 The Tricomi Operator; 4.4.3 Constant Coefficients; 4.4.4 The Characteristic Case; 4.5 Remarks and Open Problems; 4.5.1 Stability Under Perturbations; 4.5.2 Higher Order Tangential Bicharacteristics; 4.5.3 A Direct Method for Proving Carleman Estimates?; 5 Complex Coefficients and Principal Normality; 5.1 Introduction; 5.1.1 Complex-Valued Symbols; 5.1.2 Principal Normality; 5.1.3 Our Strategy for the Proof; 5.2 Pseudo-convexity and Principal Normality; 5.2.1 Pseudo-Convexity for Principally Normal Operators
000890534 5058_ $$a5.2.2 Inequalities for Symbols5.2.3 Inequalities for Elliptic Symbols; 5.3 Unique Continuation via Pseudo-convexity; 5.4 Unique Continuation for Complex Vector Fields; 5.4.1 Warm-Up: Studying a Simple Model; 5.4.2 Carleman Estimates in Two Dimensions; 5.4.3 Unique Continuation in Two Dimensions; 5.4.4 Unique Continuation Under Condition (P); 5.5 Counterexamples for Complex Vector Fields; 5.5.1 Main Result; 5.5.2 Explaining the Counterexample; 5.5.3 Comments; 6 On the Edge of Pseudo-convexity; 6.1 Preliminaries; 6.1.1 Real Geometrical Optics; 6.1.2 Complex Geometrical Optics
000890534 5058_ $$a6.2 The Alinhac-Baouendi Non-uniqueness Result6.2.1 Statement of the Result; 6.2.2 Proof of Theorem6.6; 6.3 Non-uniqueness for Analytic Non-linear Systems; 6.3.1 Preliminaries; 6.3.2 Proof of Theorem6.27; 6.4 Compact Uniqueness Results; 6.4.1 Preliminaries; 6.4.2 The Result; 6.4.3 The Proof; 6.5 Remarks, Open Problems and Conjectures; 6.5.1 Finite Type Conditions for Actual Uniqueness; 6.5.2 Ill-Posed Problems with Real-Valued Solutions; 7 Operators with Partially Analytic Coefficients; 7.1 Preliminaries; 7.1.1 Motivations; 7.1.2 Between Holmgren's and Hörmander's Theorems
000890534 506__ $$aAccess limited to authorized users.
000890534 520__ $$aOver the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation. Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book's first five chapters contain a thorough exposition of the most classical results, such as Calderón's and Hörmander's theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results between Holmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more. With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.
000890534 588__ $$aOnline resource ; title from PDF title page (viewed May 22, 2019).
000890534 650_0 $$aInequalities (Mathematics)
000890534 650_0 $$aCarleman theorem.
000890534 830_0 $$aGrundlehren der mathematischen Wissenschaften ;$$v353.
000890534 852__ $$bebk
000890534 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-15993-1$$zOnline Access$$91397441.1
000890534 909CO $$ooai:library.usi.edu:890534$$pGLOBAL_SET
000890534 980__ $$aEBOOK
000890534 980__ $$aBIB
000890534 982__ $$aEbook
000890534 983__ $$aOnline
000890534 994__ $$a92$$bISE