Universitext

Calculus of Variations

Authors: Rindler, Filip

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  • 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
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eBook 55,92 €
price for Spain (gross)
  • ISBN 978-3-319-77637-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 69,67 €
price for Spain (gross)
  • ISBN 978-3-319-77636-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field.

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.

About the authors

Filip Rindler is Associate Professor of Mathematics at the University of Warwick, UK. His research focuses on the calculus of variations and the theory of PDEs. For 2018-2023, he leads the ERC-funded SINGULARITY project.

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)

Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook 55,92 €
price for Spain (gross)
  • ISBN 978-3-319-77637-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 69,67 €
price for Spain (gross)
  • ISBN 978-3-319-77636-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Calculus of Variations
Authors
Series Title
Universitext
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-77637-8
DOI
10.1007/978-3-319-77637-8
Softcover ISBN
978-3-319-77636-1
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XII, 444
Number of Illustrations
34 b/w illustrations, 2 illustrations in colour
Topics