The Pullback Equation for Differential Forms

• Κύριοι συγγραφείς: Csató, Gyula (Συγγραφέας), Dacorogna, Bernard (Συγγραφέας), Kneuss, Olivier (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston, 2012.
• Σειρά: Progress in Nonlinear Differential Equations and Their Applications ; 83
• Θέματα: Mathematics.; Matrix theory.; Algebra.; Differential equations.; Partial differential equations.; Differential geometry.; Partial Differential Equations.; Linear and Multilinear Algebras, Matrix Theory.; Differential Geometry.; Ordinary Differential Equations.

An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map φ so that it satisfies the pullback equation: φ*(g) = f.  In more physical terms, the question under consideration can be seen as a...

Πίνακας περιεχομένων:

• Introduction
• Part I Exterior and Differential Forms
• Exterior Forms and the Notion of Divisibility
• Differential Forms
• Dimension Reduction
• Part II Hodge-Morrey Decomposition and Poincaré Lemma
• An Identity Involving Exterior Derivatives and Gaffney Inequality
• The Hodge-Morrey Decomposition
• First-Order Elliptic Systems of Cauchy-Riemann Type
• Poincaré Lemma
• The Equation div u = f
• Part III The Case k = n
• The Case f × g > 0
• The Case Without  Sign Hypothesis on f
• Part IV The Case 0 ≤ k ≤ n–1
• General Considerations on the Flow Method
• The Cases k = 0 and k = 1
• The Case k = 2
• The Case 3 ≤ k ≤ n–1
• Part V Hölder Spaces
• Hölder Continuous Functions
• Part VI Appendix
• Necessary Conditions
• An Abstract Fixed Point Theorem
• Degree Theory
• References
• Further Reading
• Notations
• Index. .