Unbounded Functionals in the Calculus of Variations

Representaion, Relaxation and Homogenization

Luciano Carbone, Riccardo De Arcangelis

394 pages, parution le 07/03/2002

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Résumé

This advanced-level monograph addresses important problems in the calculus of variations by developing the basic lines of a general theory regarding integral representation, relaxation, and homogenization for unbounded functionals. Starting with an introduction to notation and an outline of the notions of convex analysis, the authors focus on homogenization issues, describing some asymptotic behavior results and reporting some surprising new phenomena related to the Lavrentiev gap. The techniques developed recover many of the results existing in the literature. The authors' approach is unified and elegant, the text well written, and the results intriguing and useful.

Contents

Preface xi
Basic Notations and Recalls 1

1 Elements of Convex Analysis 9
2 Elements of Measure and Increasing Set Functions Theories 45
3 Minimization Methods and Variational Convergences 83
4 BV and Sobolev Spaces 107
5 Lower Semicontinuity and Minimization of Integral Functionals 137
6 Classical Results and Mathematical Models Originating Unbounded Functionals 149
7 Abstract Regularization and Jensen's Inequality 159
8 Unique Extension Results 177
9 Integral Representation for Unbounded Functionals 191
10 Relaxation of Unbounded Functionals 211
12 Homogenization of Unbounded Functionals 273
13 Homogenization of Unbounded Functionals with Special Constraints 319
14 Some Explicit Computations of Homogenized Energies in Mathematical Models Originating Unbounded Functionals

Bibliography 375
List of Symbols 389
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Luciano Carbone, Riccardo De Arcangelis
Parution	07/03/2002
Nb. de pages	394
Format	16 x 24
Couverture	Broché
Poids	698g
Intérieur	Noir et Blanc
EAN13	9781584882350
ISBN13	978-1-58488-235-0