Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc

More about us

**MathSchoolinternational** contain 5000+ of
**Mathematics Free PDF Books** and
**Physics Free PDF Books**. Which cover almost all topics for students of Mathematics, Physics and Engineering. Here is extisive list of
**Differential Equations ebooks **. We hope students and teachers like these **textbooks**, notes and solution manuals.

**Share this page:- **

**Congratulations, the link is avaliable for free download.**

**About this book :- **

**The Pullback Equation for Differential Forms ** written by
** Bernard Dacorogna, Gyula Csató, Olivier Kneuss **

In the present book we study the pullback equation for differential forms namely, given two differential k-forms f and g we want to discuss the equivalence of such forms. This turns out to be a system of nonlinear first-order partial differential equations in the unknown map ?. 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 f so that it satisfies the pullback equation: f*(g) = f. In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 = k = n–1. The present monograph provides the first comprehensive study of the equation.

The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge–Morrey decomposition and to give several versions of the Poincaré lemma. 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. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Hölder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on Hölder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation.

**Book Detail :- **
** Title: ** The Pullback Equation for Differential Forms
** Edition: **
** Author(s): ** Bernard Dacorogna, Gyula Csató, Olivier Kneuss
** Publisher: ** Birkhäuser Basel
** Series: ** Progress in Nonlinear Differential Equations and Their Applications
** Year: ** 2012
** Pages: ** 449
** Type: ** PDF
** Language: ** English
** ISBN: ** 9780817683122,0817683127
** Country: ** Switzerland

Get this Books from Amazon

**About Author :- **

The author ** Bernard Dacorogna ** is a PHD and Professor Emeritus of Statistics at the University of Florida. He is the author of Advanced Calculus with Applications in Statistics, Second Edition and co-author of Statistical Tests for Mixed Linear Models, all published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions, solution manuals or solved notes avaliable of this author, We recomended you to download all.

** • Download PDF Introduction To The Calculus Of Variations by Bernard Dacorogna **

** • Download PDF Direct Methods in the Calculus of Variations, 2E by Bernard Dacorogna **

** • Download PDF Calculus of Variations and Nonlinear PDEs by Bernard Dacorogna, Ambrosio, Caffarelli, Crandall **

** • Download PDF Implicit Partial Differential Equations by Bernard Dacorogna, Paolo Marcellini **

** • Download PDF The Pullback Equation for Differential Forms by Bernard Dacorogna, Gyula Csató, Olivier Kneuss **

** • Download PDF Vector Valued PDEs and Applications by Bernard Dacorogna, Fusco, Müller, Sverak, Ball, **
** • Download PDF Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals by Bernard Dacorogna **

** • Download PDF An Introduction to High-Frequency Finance by Bernard Dacorogna **

**Join our new updates, alerts:-**

For new updates and alerts join our WhatsApp Group and Telegram Group (you can also ask any [pdf] book/notes/solutions manual).

Join WhatsApp Group

Join Telegram Group

**Book Contents :- **
**The Pullback Equation for Differential Forms ** written by
** Bernard Dacorogna, Gyula Csató, Olivier Kneuss **
cover the following topics.

1. Introduction

Part I Exterior and Differential Forms

2. Exterior Forms and the Notion of Divisibility

3. Differential Forms

4. Dimension Reduction

Part II Hodge–Morrey Decomposition and Poincar´e Lemma

5. An Identity Involving Exterior Derivatives and Gaffney Inequality

6. The Hodge–Morrey Decomposition

7. First-Order Elliptic Systems of Cauchy–Riemann Type

8. Poincar´e Lemma

9. The Equation divu = f

10. The Case f · g > 0

11. The Case Without Sign Hypothesis on f

Part IV The Case 0 = k = n-1

13. The Cases k = 0 and k = 1

14. The Case k = 2

15. The Case 3 = k = n-1

Part V H¨older Spaces

16. H¨older Continuous Functions

Part VI Appendix

17. Necessary Conditions

18. An Abstract Fixed Point Theorem

19. Degree Theory

References

Further Reading

Notations

Index

**Note:-**

We are not the owner of this book/notes. We provide it which is already avialable on the internet. For any further querries please contact us. We never SUPPORT PIRACY. This copy was provided for students who are financially troubled but want studeing to learn. If You Think This Materials Is Useful, Please get it legally from the PUBLISHERS. Thank you.

**Related Book Categories:- **

**Other Famous Books Topics:- **

- Abstract Algebra
- Calculus
- Differential Equations
- Engineering Mathematics
- Linear Algebra
- Math Magic
- Real Analysis

**Other Topics:- **

- Basic Algebra
- Basic Mathematics
- Math History
- Math Formulas
- Mathematical Methods
- Number Theory
- Bio Mathematics
- Business Mathematics
- Probability & Statistics

**WORKSHEETS (Solved):- **

**SHORTCUT TRICKS (Division):- **

- Divisible by 2 Shortcut trick
- Divisible by 3 Shortcut trick
- Divisible by 4 Shortcut trick
- Divisible by 5 Shortcut trick
- Divisible by 6 Shortcut trick
- Divisible by 7 Shortcut trick
- Divisible by 8 Shortcut trick
- Divisible by 9 Shortcut trick
- Divisible by 10 Shortcut trick

**SHORTCUT TRICKS (Prime Number):- **

- Find the prime number from 1 to 100 just in 5 second (MATH PRIME NUMBER SHORTCUT TRICK from 1 to 100 number) ?
- Find a large number "A" is prime number or not (MATH PRIME NUMBER SHORTCUT TRICK By using Square Root method) ?
- Find the composite number from 1 to 100 just in 5 second (MATH COMPOSITE NUMBER SHORTCUT TRICK from 1 to 100 number) ?