Direct Methods in the Calculus of Variations

AvBernard Dacorogna

Inbunden, Engelska, 2007

Del i serien Applied Mathematical Sciences

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Beskrivning

This second edition is the successor to "Direct methods in the calculus of variations" which was published in the Applied Mathematical Sciences series and is currently out of print. Although the core and the structure of the present book is similar to the first edition, it is much more than a revised version. Fifteen years have passed since the publication of the "Direct methods in the calculus of variations" book and since the subject is a very active one, almost half of the book presently consists of new material. The perspective has also slightly changed, indeed, a new subject, "quasiconvex analysis" has now been developed. The present edition, which is essentially a reference book on the subject of quasiconvex analysis can be used, as was the earlier book, for an advanced course on the calculus of variations.

Produktinformation

Utgivningsdatum:2007-11-29
Mått:155 x 235 x 34 mm
Vikt:980 g
Format:Inbunden
Språk:Engelska
Serie:Applied Mathematical Sciences
Antal sidor:622
Upplaga:2
Förlag:Springer-Verlag New York Inc.
ISBN:9780387357799

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

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 fur Mathematik, Vol. 160 (4), July, 2010)

Innehållsförteckning

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.