Direct Methods in the Calculus of Variations: v. 78 (Applied Mathematical Sciences) - Hardcover

Dacorogna, Bernard

Hardcover

ISBN 10: 3540504915 ISBN 13: 9783540504917

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1989

Synopsis

This book deals with the calculus of variations and presents the so called direct methods for proving existence of minima. It is divided into four main parts. The first one deals with the scalar case, i.e. with real-valued functions; it gives well known existence theorems and studies some of the classical necessary conditions such as Euler equations. The second part is concerned with vector-valued functions; some necessary or sufficient conditions are studied as well as several examples. The third one deals with the relaxation of nonconvex problems. Finally in the Appendix several examples of applications of the previous chapters to nonlinear elasticity and optimal design are given. The book serves an important purpose in bringing together, in the second and third parts as well as the Appendix, material which till now remained scattered in the literature. It thus gives a unified view of some of the recent developments. As special emphasis is laid on examples throughout, it will be useful also to readers interested in applications.

About this title

Review

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)

From the Back Cover

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.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1989
• Language: English
• ISBN 10: 3540504915
• ISBN 13: 9783540504917
• Binding: Hardcover
• Number of pages: 317