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One-dimensional Variational Problems : An Introduction - Giuseppe Buttazzo

One-dimensional Variational Problems

An Introduction

Hardcover Published: 1st April 2000
ISBN: 9780198504658
Number Of Pages: 270

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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 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.

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

ISBN: 9780198504658
ISBN-10: 0198504659
Series: Oxford Lecture Series in Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 270
Published: 1st April 2000
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.1 x 16.2  x 2.1
Weight (kg): 0.55