Items related to The Pullback Equation for Differential Forms
Synopsis
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.
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About the Author
Csato, Dacorogna, and Kneuss teach at Ecole Polytechnique Fédérale de Lausanne in Switzerland.
Review
From the reviews:
“This monograph provides a systematic study of the pullback equation, presenting results on local and global existence of solutions and regularity. ... It is very likely that this book will become an indispensable reference and source of inspiration for everybody interested in this subject. ... The book starts with an introductory chapter which serves as a user’s guide for the rest of the book ... . The book is completed by an index and a list of references consisting of over 100 entries.” (Pietro Celada, Mathematical Reviews, April, 2013)
“This book studies the pullback equation for differential forms ... . The principal emphasis of this book is put upon regularity and boundary conditions. Special attention has been paid upon getting optimal regularity, which requires estimates for elliptic equations and fine properties of Hölder spaces. The book will presumably appeal to both geometers and analysts.” (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1247, 2012)
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