One-dimensional Variational Problems

Giuseppe Buttazzo, Mariano Giaquinta, Stefan Hildebrandt

ISBN 10: 0198504659 / ISBN 13: 9780198504658

Published by Oxford University Press, GB, 1999

About this Item

One-dimensional variational problems have been somewhat neglected in the literature on calculus of variations, as authors usually treat minimal problems for multiple integrals which lead to partial differential equations and are considerably more difficult to handle. One-dimensional problems are connected with ordinary differential equations, and hence need many fewer technical prerequisites, but they exhibit the same kind of phenomena and surprises as variational problems for multiple integrals. This book provides an modern introduction to this subject, placing special emphasis on direct methods. It combines the efforts of a distinguished team of authors who are all renowned mathematicians and expositors. Since there are fewer technical details graduate students who want an overview of the modern approach to variational problems will be able to concentrate on the underlying theory and hence gain a good grounding in the subject. Except for results from the theory of measure and integration and from the theory of convex functions, the text develops all mathematical tools needed, including the basic results on one-dimensional Sobolev spaces, absolutely continuous functions, and functions of bounded variation.

Seller Inventory # LU-9780198504658

Bibliographic Details

• Title: One-dimensional Variational Problems
• Publisher: Oxford University Press, GB
• Publication Date: 1999
• Language: English
• ISBN 10: 0198504659
• ISBN 13: 9780198504658
• Binding: Hardback
• Condition: New
• Weight: 548 grams

About this title

Synopsis

One-dimensional variational problems are often neglected in favor of problems which use multiple integrals and partial differential equations, which are typically more difficult to handle. However, these problems and their associated ordinary differential equations do exhibit many of the same challenges and complexity of higher-dimensional problems, while being accessible to more students. This book for graduate students provides the first modern introduction to this subject. It emphasizes direct methods and provides an exceptionally clear view of the underlying theory. Except for standard material on measures, integration and convex functions, the book develops all of the necessary mathematical tools, including basic results for one-dimensional Sobolev spaces, absolutely continuous functions, and functions of bounded variation.

About the Author

Stefan Hildebrandt is Professor of Mathematics at the University of Bonn.