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Direct Methods in the Calculus of Variations

  • Book
  • © 2008

Overview

Authors:
  1. Bernard Dacorogna

    1. Ecole Polytechnique Federale de Lausanne, CH–1015, Switzerland

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  • Applications included
  • The subject is a very active one, almost half of the book consists of new materials
  • Includes supplementary material: sn.pub/extras

Part of the book series: Applied Mathematical Sciences (AMS, volume 78)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii
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  2. Convex analysis and the scalar case

    1. Introduction

      Pages 1-27

    2. Convex sets and convex functions

      Pages 31-71

    3. Lower semicontinuity and existence theorems

      Pages 73-117

    4. The one dimensional case

      Pages 119-151

  4. Relaxation and non-convex problems

    1. Relaxation theorems

      Pages 415-437

    2. Implicit partial differential equations

      Pages 439-463

    3. Existence of minima for non-quasiconvex integrands

      Pages 465-499

  6. Back Matter

    Pages 569-621
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Keywords

About this book

This book studies vectorial problems in the calculus of variations and quasiconvex analysis. It is a new edition of the earlier book published in 1989 and has been updated with some new material and examples added.

This monograph will appeal to researchers and graduate students in mathematics and engineering.

Reviews

From the reviews of the second edition:

"This new edition is very much expanded, up to the point that it can be considered an almost entirely new book. … I was a PhD student in the early 90’s, and I have been studying and using it continuously since then. It has accompanied me and many others as a valuable source for results and as a standard reference on the subject. I am sure that this new edition will be serving in the same role as well." (Pietro Celada, Mathematical Reviews, Issue 2008 m)

"The present monograph has been … a ‘revised and augmented edition to Direct Methods in the Calculus of Variations’. … the author maintains a fresh and lucid style, resulting in a concise, very well readable presentation. Surely this book will define a long-lasting standard in its area. … The exhaustive bibliography comprises 621 references and covers the relevant publications in the area … ." (Marcus Wagner, Zentralblatt MATH, Vol. 1140, 2008)

“This is a substantially extended new edition of the author’s introduction to direct methods in the calculus of variations. … The author has taken great care to include all the main developments in the area since the first edition (the list of references comprises 621 items). The book is carefully written and provides a very readable introduction to the field.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 160 (4), July, 2010)

Authors and Affiliations

  • Ecole Polytechnique Federale de Lausanne, CH–1015, Switzerland

    Bernard Dacorogna

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