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
02 December 2019

Differential calculus & equations; Applied mathematics; Mathematical physics

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 Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9780367455071
ISBN 10: 0367455072
Pages: 408
Publication Date: 02 December 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Carbone, Luciano; De Arcangelis, Riccardo