Druet / Hebey / Robert Blow-up Theory for Elliptic PDEs in Riemannian Geometry

Course Book
ISBN: 978-1-4008-2616-2
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 45, 224 Seiten

Reihe: Mathematical Notes

No detailed description available for "Blow-up Theory for Elliptic PDEs in Riemannian Geometry".

Autoren/Hrsg.

Druet, Olivier

Hebey, Emmanuel

Robert, Frédéric

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

Preface vii

Chapter 1. Background Material 1

1.1 Riemannian Geometry 1

1.2 Basics in Nonlinear Analysis 7

Chapter 2. The Model Equations 13

2.1 Palais-Smale Sequences 14

2.2 Strong Solutions of Minimal Energy 17

2.3 Strong Solutions of High Energies 19

2.4 The Case of the Sphere 23

Chapter 3. Blow-up Theory in Sobolev Spaces 25

3.1 The H 2/1-Decomposition for Palais-Smale Sequences 26

3.2 Subtracting a Bubble and Nonnegative Solutions 32

3.3 The De Giorgi-Nash-Moser Iterative Scheme for Strong Solutions 45

Chapter 4. Exhaustion and Weak Pointwise Estimates 51

4.1 Weak Pointwise Estimates 52

4.2 Exhaustion of Blow-up Points 54

Chapter 5. Asymptotics When the Energy Is of Minimal Type 67

5.1 Strong Convergence and Blow-up 68

5.2 Sharp Pointwise Estimates 72

Chapter 6. Asymptotics When the Energy Is Arbitrary 83

6.1 A Fundamental Estimate: 1 88

6.2 A Fundamental Estimate: 2 143

6.3 Asymptotic Behavior 182

Appendix A. The Green's Function on Compact Manifolds 201

Appendix B. Coercivity Is a Necessary Condition 209

Bibliography 213

Über Autor(innen)

Olivier Druet is Researcher at CNRS, Ecole Normale Supérieure de Lyon. Emmanuel Hebey is Professor at Université de Cergy-Pontoise. Frédéric Robert is Associate Professor at Université de Nice Sophia-Antipolis.