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Homogenization of Multiple Integrals

Homogenization of Multiple Integrals (Hardback)

By Braides, Andrea
By Defranceschi, Anneliese

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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 c...ellular 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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ISBN 9780198502463
Released NZ 1 Aug 1998
Publisher Oxford University Press
Format Hardback
Series Oxford Lecture Series in Mathematics & Its Applications (part: 12)
Available at publisher; allow 3-6 weeks delivery due to Covid 19 freight delays

Full details for this title

ISBN-13 9780198502463
Stock Available
Status Available at publisher; allow 3-6 weeks delivery due to Covid 19 freight delays
Publisher Oxford University Press
Imprint Clarendon Press
Released 1 Aug 1998
Publication Country United Kingdom United Kingdom
Format Hardback
Author(s) By Braides, Andrea
By Defranceschi, Anneliese
Series Oxford Lecture Series in Mathematics & Its Applications (part: 12)
Category Mathematics: Functional Analysis
Differential Equations
Integral Equations
Calculus Of Variations
Numerical Analysis
Mathematics For Scientists & Engineers
Mathematical Modelling
Analytical Mechanics (Physics)
Number of Pages 312
Dimensions Width: 163mm
Height: 241mm
Spine: 24mm
Dewey Code 515.43
Weight 642g
Interest Age General Audience
Reading Age General Audience
Library of Congress Multiple integrals, Homogenization (Differential equations)
NBS Text Mathematics
ONIX Text Professional and scholarly