Direct Methods in the Calculus of Variations
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ISBN-13:
9781441922595
Veröffentl:
2010
Einband:
Paperback
Erscheinungsdatum:
29.11.2010
Seiten:
636
Autor:
Bernard Dacorogna
Gewicht:
949 g
Format:
235x155x34 mm
Serie:
78, Applied Mathematical Sciences
Sprache:
Englisch
Beschreibung:
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.
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.
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