Hugendubel.info - Die B2B Online-Buchhandlung 

Merkliste
Die Merkliste ist leer.
Bitte warten - die Druckansicht der Seite wird vorbereitet.
Der Druckdialog öffnet sich, sobald die Seite vollständig geladen wurde.
Sollte die Druckvorschau unvollständig sein, bitte schliessen und "Erneut drucken" wählen.

The Pullback Equation for Differential Forms

BuchGebunden
Englisch
Birkhäuser Bostonerschienen am12.11.20112012
The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 ⤠k ⤠n-1. The core of the book discusses the case k = n, and then the case 1⤠k ⤠n-1 with special attention on the case k = 2, which is fundamental in symplectic geometry.mehr
Verfügbare Formate
BuchGebunden
EUR58,84
E-BookPDF1 - PDF WatermarkE-Book
EUR128,39

Produkt

KlappentextThe problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 ⤠k ⤠n-1. The core of the book discusses the case k = n, and then the case 1⤠k ⤠n-1 with special attention on the case k = 2, which is fundamental in symplectic geometry.
Zusammenfassung
The only book to systematically explore the equivalence of differential forms

Rigorously presents Hodge decomposition and several versions of the Poincaré lemma

Includes a very rare, extended study of Hölder spaces

Useful resource for graduate students and researchers, requiring only an elementary knowledge of differential geometry and partial and ordinary differential equations

Includes supplementary material: sn.pub/extras

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr
Kritik
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)mehr