Calculus of Variations by Xianqing Lijost

Calculus of Variations by Xianqing Lijost

This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues like Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais-Smale condition. The only prerequisites are basic results from calculus of one and several variables. After having studied this book, the reader will be well-equipped to read research papers in the calculus of variations.

"This modern self-contained exposition..is an excellent textbook for graduate students and a good source of information in the calculus of variations." Mathematical Reviews

SKU	Nicht verfügbar
ISBN 13	9780521642033
ISBN 10	0521642035
Titel	Calculus of Variations
Autor	Xianqing Lijost
Serie	Cambridge Studies In Advanced Mathematics
Buchzustand	Nicht verfügbar
Bindungsart	Hardback
Verlag	Cambridge University Press
Erscheinungsjahr	1999-01-28
Seitenanzahl	340
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.