Direct Methods in the Calculus of Variations [electronic resource] / by Bernard Dacorogna.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Applied Mathematical Sciences: 78Publisher: New York, NY : Springer New York, 2008Description: XII, 622 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387552491Subject(s): Mathematics | Partial differential equations | Calculus of variations | Mathematics | Partial Differential Equations | Calculus of Variations and Optimal Control; OptimizationAdditional physical formats: Printed edition:: No titleDDC classification: 515.353 LOC classification: QA370-380Online resources: Click here to access online
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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.