Unbounded Functionals in the Calculus of Variations: Representation, Relaxation, and Homogenization

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Luciano Carbone Riccardo De Arcangelis

Unbounded Functionals in the Calculus of Variations

Representation, Relaxation, and Homogenization

Luciano Carbone, Riccardo De Arcangelis

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English

Chapman & Hall/CRC
12 December 2001

Functional analysis & transforms; Integral calculus & equations

Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals

of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a general theory of integral representation, relaxation, and homogenization for unbounded functionals. The first part of the

book builds the foundation for the general theory with concepts and tools from convex analysis, measure theory, and the

theory of variational convergences. The authors then introduce some function spaces and explore some lower semicontinuity and minimization problems for energy functionals. Next, they survey some specific aspects the theory of standard functionals.

The second half of the book carefully develops a theory of unbounded, translation invariant functionals that leads to results deeper than those already known, including unique extension properties, representation as integrals of the

calculus of variations, relaxation theory, and homogenization processes. In this study, some new phenomena are pointed out. The authors' approach is unified and elegant, the text well written, and the results intriguing and useful, not just

in various fields of mathematics, but also in a range of applied mathematics, physics, and material science disciplines.

By: Luciano Carbone, Riccardo De Arcangelis
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Volume: 125
Dimensions: Height: 234mm, Width: 156mm, Spine: 28mm
Weight: 698g
ISBN: 9781584882350
ISBN 10: 1584882352
Pages: 408
Publication Date: 12 December 2001
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Carbone, Luciano; De Arcangelis, Riccardo