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Direct Methods in the Calculus of Variations de Bernard Dacorogna

Direct Methods in the Calculus of Variations: Applied Mathematical Sciences, cartea 78

Autor Bernard Dacorogna
en Limba Engleză Hardback – 29 noi 2007
This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.
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Specificații

ISBN-13: 9780387357799
ISBN-10: 0387357793
Pagini: 619
Ilustrații: XII, 622 p.
Dimensiuni: 155 x 235 x 34 mm
Greutate: 0.98 kg
Ediția:2nd ed. 2008
Editura: Springer
Colecția Springer
Seria Applied Mathematical Sciences

Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

Convex analysis and the scalar case.- Convex sets and convex functions.- Lower semicontinuity and existence theorems.- The one dimensional case.- Quasiconvex analysis and the vectorial case.- Polyconvex, quasiconvex and rank one convex functions.- Polyconvex, quasiconvex and rank one convex envelopes.- Polyconvex, quasiconvex and rank one convex sets.- Lower semi continuity and existence theorems in the vectorial case.- Relaxation and non-convex problems.- Relaxation theorems.- Implicit partial differential equations.- Existence of minima for non-quasiconvex integrands.- Miscellaneous.- Function spaces.- Singular values.- Some underdetermined partial differential equations.- Extension of Lipschitz functions on Banach spaces.

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

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

Descriere

Descriere de la o altă ediție sau format:

This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.