One-dimensional variational problems : an introduction
著者
書誌事項
One-dimensional variational problems : an introduction
（Oxford lecture series in mathematics and its applications, 15）
Clarendon Press, 1998
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注記
"Oxford science publications"--Cover
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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
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