One-dimensional Variational Problems: An Introduction

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Clarendon Press, 1998 - Mathematics - 262 pages
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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 problemsare 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 ondirect 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 underlyingtheory 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 continuousfunctions, and functions of bounded variation.
 

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Contents

Section 1
1
Section 2
7
Section 3
10
Section 4
44
Section 5
46
Section 6
49
Section 7
50
Section 8
51
Section 21
119
Section 22
124
Section 23
126
Section 24
128
Section 25
134
Section 26
149
Section 27
152
Section 28
156

Section 9
54
Section 10
68
Section 11
73
Section 12
82
Section 13
83
Section 14
85
Section 15
86
Section 16
87
Section 17
97
Section 18
104
Section 19
107
Section 20
110
Section 29
166
Section 30
167
Section 31
171
Section 32
179
Section 33
188
Section 34
189
Section 35
203
Section 36
218
Section 37
225
Section 38
236
Section 39
246
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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.

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