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＜E-Book＞
Direct Methods in the Calculus of Variations / by Bernard Dacorogna
(Applied Mathematical Sciences. ISSN:2196968X ; 78)

Edition	2nd ed. 2008.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2008
Size	XII, 622 p : online resource
Authors	*Dacorogna, Bernard author SpringerLink (Online service)
Subjects	LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations FREE:Differential Equations FREE:Calculus of Variations and Optimization
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-0-387-55249-1

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