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direct methods in calculus variations bernard dacorogna [pdf]

Direct Methods in the Calculus of Variations, 2E by Bernard Dacorogna

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About this book :-
Direct Methods in the Calculus of Variations, 2E written by Bernard Dacorogna
This book is a new edition of the authors previous book entitled Direct Methods in the Calculus of Variations, 1989. It is devoted to the study of vectorial problems in the calculus of variations. The book has been updated significantly and a number of additional examples have been included. The book will appeal researchers and graduate students in mathematics and engineering. The calculus of variations is an immense and very active field. It is therefore, when writing a book, necessary to make a severe selection. This was already the case for [179] and is even more so for this new edition. Rather than superficially covering a lot of materials, I preferred to privilege only some aspects of the field. Here are some main features of the book. I strongly emphasized the resemblances between convex and quasiconvex analysis as well as the “algebraic” aspect of the field, notably through the determinants and singular values. Besides the classical results on lower semicontinuity and relaxation, an important feature of the monograph is the emphasis on the existence of minimizers for non convex problems.

Book Detail :-
Title: Direct Methods in the Calculus of Variations
Edition: 2nd
Author(s): Bernard Dacorogna
Publisher: Springer
Series: Applied Mathematical Sciences
Year: 2007
Pages: 624
Type: PDF
Language: English
ISBN: 0387357793,9780387357799,9780387552491
Country: Switzerland
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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.

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Book Contents :- Direct Methods in the Calculus of Variations, 2E written by Bernard Dacorogna cover the following topics.
1. Introduction
I-Convex analysis and the scalar case
2. Convex sets and convex functions
3. Lower semicontinuity and existence theorems
4. The one dimensional case
II-Quasiconvex analysis and the vectorial case
5. Polyconvex, quasiconvex and rank one convex functions
6. Polyconvex, quasiconvex and rank one convex envelopes
7. Polyconvex, quasiconvex and rank one convex sets
8. Lower semi continuity and existence theorems in the vectorial case
III-Relaxation and non-convex problems
9. Relaxation theorems
10. Implicit partial differential equations
11. Existence of minima for non-quasiconvex integrands
12. Function spaces
13. Singular values
14. Some underdetermined partial differential equations
15 Extension of Lipschitz functions on Banach spaces


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