Synopses & Reviews
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.
Synopsis
While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first modern introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.
Description
Includes bibliographical references (p. [246]-259) and index.
Table of Contents
Introduction
1. Classical problems and indirect methods
2. Absolutely continuous functions and Sobolev spaces
3. Semicontinuity and existence results
4. Regularity of minimizers
5. Some applications
6. Scholia
References
Index