Introduction to Global Variational Geometry

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Elsevier, Apr 1, 2000 - Mathematics - 500 pages
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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups.

The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.

Featured topics

- Analysis on manifolds
- Differential forms on jet spaces
- Global variational functionals
- Euler-Lagrange mapping
- Helmholtz form and the inverse problem
- Symmetries and the Noether’s theory of conservation laws
- Regularity and the Hamilton theory
- Variational sequences
- Differential invariants and natural variational principles

- First book on the geometric foundations of Lagrange structures
- New ideas on global variational functionals
- Complete proofs of all theorems
- Exact treatment of variational principles in field theory, inc. general relativity
- Basic structures and tools: global analysis, smooth manifolds, fibred spaces
 

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Contents

Chapter 1 Interpolation Theory in Banach Spaces
15
Chapter 2 LebesgueBesov Spaces without Weights in Rn and R+n
151
Chapter 3 LebesgueBesov Spaces with Weigths in Domains
245
Chapter 4 LebesgueBesov Spaces without Weigths in Domains
309
Chapter 5 Regular Elliptic Differential Operators
361
Chapter 6 Strongly Degenerate Elliptic Differential Operators
405
Chapter 7 Legendre and Tricomi Differential Operators
429
Chapter 8 Nuclear Function Spaces
476
Bibliography
483
Table of Symbols
519
Author Index
522
Subject Index
527
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