One-dimensional Variational Problems: An Introduction

Front Cover
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.
 

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Contents

Section 1
10
Section 2
42
Section 3
44
Section 4
46
Section 5
49
Section 6
50
Section 7
51
Section 8
52
Section 12
83
Section 13
104
Section 14
127
Section 15
134
Section 16
156
Section 17
180
Section 18
181
Section 19
195

Section 9
53
Section 10
54
Section 11
82
Section 20
225
Section 21
246
Copyright

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About the author (1998)

Giuseppe Buttazzo and Mariano Giaquinta are both at University of Pisa. Stefan Hildebrandt is at University of Bonn.