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OverviewOne-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. Full Product DetailsAuthor: Giuseppe Buttazzo (Professor, Professor) , Mariano Giaquinta (Professor, Professor, both at University of Pisa, Italy) , Stefan Hildebrandt (Professor, Professor, University of Bonn, Germany)Publisher: Oxford University Press Imprint: Oxford University Press Volume: 15 Dimensions: Width: 16.20cm , Height: 2.10cm , Length: 24.10cm Weight: 0.548kg ISBN: 9780198504658ISBN 10: 0198504659 Pages: 270 Publication Date: 28 January 1999 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsIntroduction 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: ScholiaReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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