Direct Methods in the Calculus of Variations

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Springer Science & Business Media, Nov 21, 2007 - Mathematics - 622 pages

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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Contents

Polyconvex quasiconvex and rank one convex sets
7
integrands
20
Convex analysis and the scalar case
29
Lower semicontinuity and existence theorems
73
The one dimensional case 119
118
5
153
Polyconvex quasiconvex and rank one convex envelopes
265
Lower semi continuity and existence theorems in
367
Existence of minima for nonquasiconvex integrands
465
Function spaces
503
Singular values
514
Some underdetermined partial differential equations
534
Extension of Lipschitz functions on Banach spaces
548
Bibliography
569
Notation
576
347
592

Relaxation theorems
415
Implicit partial differential equations 439
438
529
603
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