© 2008

Direct Methods in the Calculus of Variations


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

Table of contents

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

  3. Quasiconvex analysis and the vectorial case

  4. Relaxation and non-convex problems

  5. Miscellaneous

  6. Back Matter
    Pages 569-621

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.


Calculus of Variations Dacorogna Direct Methods Variations calculus differential equation minimum partial differential equation

Authors and affiliations

  1. 1.Ecole Polytechnique Federale de LausanneCH–1015Switzerland

Bibliographic information

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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)