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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.

Product Specifications

Format: paperback
ASIN: 0821894137
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Functional Analysis
Domain: Amazon UK
Release Date: 28 February 2013
Listed Since: 12 March 2015

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

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

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