Calculus of Variations: 64 (Cambridge Studies in Advanced Mathematics)

Book Details

• Publisher: Cambridge University Press

• Author: Jurgen Jost

• Language: English

• Edition: 1st Edition

• ISBN: 9780521057127

• Pages: 340

• Cover: Paperback

• Dimensions: 8.9 x 5.7 x 1.1 inches

About The Book

Jurgen Jost's Calculus of Variations offers a comprehensive and modern introduction to this important area of mathematical theory, guiding the reader from basic concepts to advanced topics. The book begins with classical issues such as Euler-Lagrange equations, leading to more contemporary discussions including Noether's theorem, Hamilton-Jacobi theory, and geodesic lines. It further explores the geometric and topological aspects of the theory while introducing the fundamental ideas of optimal control theory.

In the second part of the book, Jost delves into multiple integrals, reviewing Lebesgue integration, Banach and Hilbert space theory, and Sobolev spaces with complete proofs. The book also addresses direct methods, lower semicontinuity theorems, and modern concepts like relaxation, Gamma convergence, bifurcation theory, and minimax methods based on the Palais-Smale condition. Designed for graduate students, this textbook is a valuable resource for those aiming to engage with the latest research in the calculus of variations.