Sinossi
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.
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Informazioni sull?autore
Stefan Hildebrandt is Professor of Mathematics at the University of Bonn.
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One-dimensional Variational Problems: An Introduction: 15 (Oxford Lecture Series in Mathematics and Its Applications)
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One-Dimensional Variational Problems: An Introduction (Oxford Lecture Series in Mathematics and Its Applications)
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One-Dimensional Variational Problems: An Introduction (Oxford Lecture Series in Mathematics and Its Applications)
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Oxford Clarendon Press, 1998
ISBN 10: 0198504659
ISBN 13: 9780198504658
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One-Dimensional Variational Problems: An Introduction
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One-Dimensional Variational Problems: An Introduction
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Condizione: Sehr gut. Zustand: Sehr gut | Seiten: 272 | Sprache: Englisch | Produktart: Bücher | 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. Codice articolo 1353464/202
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