Homogenization of Multiple Integrals: 12 - Rilegato

Braides, Andrea; Defranceschi, Anneliese

Rilegato

ISBN 10: 019850246X ISBN 13: 9780198502463

Casa editrice: OUP Oxford, 1998

Riassunto

The object of homogenization theory is the description of the macroscopic properties of structures with fine microstructure, covering a wide range of applications that run from the study of properties of composites to optimal design. The structures under consideration may model cellular elastic materials, fibred materials, stratified or porous media, or materials with many holes or cracks. In mathematical terms, this study can be translated in the asymptotic analysis of fast-oscillating differential equations or integral functionals. The book presents an introduction to the mathematical theory of homogenization of nonlinear integral functionals, with particular regard to those general results that do not rely on smoothness or convexity assumptions. Homogenization results and appropriate descriptive formulas are given for periodic and almost- periodic functionals. The applications include the asymptotic behaviour of oscillating energies describing cellular hyperelastic materials, porous media, materials with stiff and soft inclusions, fibered media, homogenization of HamiltonJacobi equations and Riemannian metrics, materials with multiple scales of microstructure and with multi-dimensional structure. The book includes a specifically designed, self-contained and up-to-date introduction to the relevant results of the direct methods of Gamma-convergence and of the theory of weak lower semicontinuous integral functionals depending on vector-valued functions. The book is based on various courses taught at the advanced graduate level. Prerequisites are a basic knowledge of Sobolev spaces, standard functional analysis and measure theory. The presentation is completed by several examples and exercises.

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Contenuti

• Preface
• Contents
• Introduction
• Notation
• Part I: Lower Semicontinuity
• 1: Lower semicontinuity and coerciveness
• 2: Weak convergence
• 3: Minimum problems in sobolev spaces
• 4: Necessary conditions for weak lower semicontinuity
• 5: Sufficient conditions for weak lower semicontinuity
• Part II: Gamma-convergence
• 6: The structure of quasiconvex functions
• 7: A naive introduction of Gamma-convergence
• 8: The indirect methods of Gamma-convergence
• 9: Direct methods - an integral representation result
• 10: Increasing set functions
• 11: The fundamental estimate
• 12: Integral functionals with standard growth condition
• Part III: Basic Homogenization
• 13: A one-dimensional example
• 14: Periodic homogenization
• 15: Almost periodic homogenization
• 16: Two applications
• 17: A closure theorem for the homogenization
• 18: Loss of polyconvexity by homogenization
• Part IV: Finer Homogenization Results
• 19: Homogenization of connected media
• 20: Homogenization with stiff and soft inclusions
• 21: Homogenization with non-standard growth conditions
• 22: Iterated homogenization
• 23: Correctors for the homogenization
• 24: Homogenization of multi-dimensional structures
• Part V: Appendices
• A Almost periodic functions
• B Construction of extension operators
• C Some regularity results
• References
• Index

Dettagli dell'edizione

• Editore: OUP Oxford
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 019850246X
• ISBN 13: 9780198502463
• Rilegatura: Copertina rigida
• Numero di pagine: 312
• Contatto del produttore: Messaggerie Libri; ufficio.anagrafiche@meli.it; ; Via Verdi, 8.; Assago Milano; 20090; Italia