ENGLISH

Calculus of Variations and Harmonic Maps (Translations of Mathematical Monographs)

By Hajime Urakawa

Book information

Publisher
American Mathematical Society
Year
1993
ISBN
0821845810, 9780821845813
LCC
QA315 .U7313 1993
Open Library ID
OL1422262M
Language
english
Format
PDF
Filesize
5 MB (4819380 bytes)
Series
Translations of Mathematical Monographs
Pages
271\271
Scanned
yes
Time added
2010-05-31 15:29:46

Description

This book provides a wide view of the calculus of variations as it plays an essential role in various areas of mathematics and science. Containing many examples, open problems, and exercises with complete solutions, the book would be suitable as a text for graduate courses in differential geometry, partial differential equations, and variational methods. The first part of the book is devoted to explaining the notion of (infinite-dimensional) manifolds and contains many examples. An introduction to Morse theory of Banach manifolds is provided, along with a proof of the existence of minimizing functions under the Palais-Smale condition. The second part, which may be read independently of the first, presents the theory of harmonic maps, with a careful calculation of the first and second variations of the energy. Several applications of the second variation and classification theories of harmonic maps are given.

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