Direct Methods in the Calculus of Variations

Direct Methods in the Calculus of Variations

by Bernard Dacorogna

Paperback(Softcover reprint of hardcover 2nd ed. 2008)

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Overview

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.

Product Details

ISBN-13: 9781441922595
Publisher: Springer New York
Publication date: 11/29/2010
Series: Applied Mathematical Sciences , #78
Edition description: Softcover reprint of hardcover 2nd ed. 2008
Pages: 622
Product dimensions: 6.10(w) x 9.25(h) x 0.05(d)

Table of Contents

Introduction.- 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.- Bibliography.- Index.- Notations.

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