Carleman inequalities : an introduction and more /: an introduction and more. ([2019])
- Record Type:
- Book
- Title:
- Carleman inequalities : an introduction and more /: an introduction and more. ([2019])
- Main Title:
- Carleman inequalities : an introduction and more
- Further Information:
- Note: Nicolas Lerner.
- Authors:
- Lerner, Nicolas, 1953-
- Contents:
- Intro; 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 3 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 4.4.1 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; 5.1Intro; 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 3 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 4.4.1 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 5.2.2 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 6.2 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 … (more)
- Publisher Details:
- Cham : Springer
- Publication Date:
- 2019
- Copyright Date:
- 2019
- Extent:
- 1 online resource
- Subjects:
- 515/.26
Inequalities (Mathematics)
Carleman theorem
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9783030159931
3030159930 - Related ISBNs:
- 9783030159924
- Notes:
- Note: Includes bibliographical references and index.
Note: Online resource ; title from PDF title page (EBSCO, viewed May 22, 2019). - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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- Physical Locations:
- British Library HMNTS - ELD.DS.425970
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