The Pullback Equation for Differential Forms (Hardcover)

Introduction.- Part I Exterior and Differential Forms.- Exterior Forms and the Notion of Divisibility.- Differential Forms.- Dimension Reduction.- Part II Hodge-Morrey Decomposition and Poincare Lemma.- An Identity Involving Exterior Derivatives and Gaffney Inequality.- The Hodge-Morrey Decomposition.- First-Order Elliptic Systems of Cauchy-Riemann Type.- Poincare 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 Holder Spaces.- Holder Continuous Functions.- Part VI Appendix.- Necessary Conditions.- An Abstract Fixed Point Theorem.- Degree Theory.- References.- Further Reading.- Notations.- Index.?