One-Dimensional Variational Problems An Introduction

Klappentext 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. Zusammenfassung This book combines the efforts of a distinguished team of authors, who are all renowned mathematicians and expositors, and provides a modern introduction to the calculus of variations. By focusing on the one-dimensional case it remains relatively free of technicalities, and therefore provides a useful overview of the theory at a level suitable for graduate students. Inhaltsverzeichnis 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

Product details

• Authors: Giuseppe Giaquinta Buttazzo, Giaquinta Mariano, Buttazzo Giuseppe, Giuseppe (Professor Buttazzo, Stefan Hildebrandt, Mariano Giaquinta, Giuseppe Buttazzo
• Publisher: Oxford University Press
• Content: Book
• Product form: Hardback
• Publication date: 28.01.1999
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis
• EAN: 9780198504658
• ISBN: 978-0-19-850465-8
• Pages: 270
• Series: Oxford Lecture Series in Mathematics and Its Applications > 15; Oxford Lecture Series in Mathe > 15; Oxford Lecture Series in Mathematics and Its Applications > 15; Oxford Lecture Mathematics and > 15
• Subjects: MATHEMATICS / Applied, SCIENCE / Mechanics / General, MATHEMATICS / Differential Equations / General, MATHEMATICS / Functional Analysis, Differential calculus & equations, Applied mathematics, Calculus of variations, Differential calculus and equations, Analytical mechanics