Overview
- Presents several strands of the most recent research on the calculus of variations
- Builds on powerful analytical techniques such as Young measures to provide the reader with an effective toolkit for the analysis of variational problems in the vectorial setting
- Includes 120 exercises to consolidate understanding
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (13 chapters)
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Front Matter
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Basic Course
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Front Matter
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Advanced Topics
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Front Matter
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Back Matter
Keywords
About this book
Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored.
While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.
Reviews
“The purpose of this textbook is to give a comprehensive introduction to the classical and modern calculus of variations; it serves as useful reference to advanced undergraduate and graduate students as well as researchers in the field. … This book is interesting to a reading seminar or a companion for self-study.” (Hengyou Lan, zbMATH 1402.49001, 2019)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Calculus of Variations
Authors: Filip Rindler
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-77637-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-77636-1Published: 29 June 2018
eBook ISBN: 978-3-319-77637-8Published: 20 June 2018
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XII, 444
Number of Illustrations: 34 b/w illustrations, 2 illustrations in colour
Topics: Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations, Functional Analysis, Mathematical Applications in the Physical Sciences